Ennetech by Erasmus and Kinkajou Authors

 

 

Erasmus and Kinkajou share their vision of technologies that will help us on our way.

Subatomic Particle Theory of the Atom

 

 

The subatomic components of atoms were inferred from experiments in early 20th Century.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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KinkajouKinkajou : This stuff is really complicated. I think unlike many of our topics, most of our audience really have no basis of understanding anything about quantum science as it is so far away from their daily experience.
ErasmusErasmus : I agree. I will introduce this topic, by first summarising what we know about the quantum world and how we arrived at knowing this.  I will look at what we believe and how experimental science underpins what we believe.


Quantum phenomena occur at incredibly high energy states. We’re not used to thinking about how energetic these phenomena are, because we consider them often only in the context of single atoms or of subatomic elements.

There are however natural phenomena where these astronomically high energy states do occur. Quantum science is incredibly important in explaining many astronomical phenomena. So we will visit astronomy to look at quantum physics and how it affects the universe.

Finally I will summarise the significant quantum effects that scientists have observed and look at their relevance to human technology, present and future.

 



KinkajouKinkajou : that sounds like a good way to cover such a complex topic. I suppose we should start with the development subatomic theory. Once upon a time, just prior to the early 1900s, humanity believed that the physical world was built of atoms.

Atoms were smallest component of matter. They could be seen as little round balls that were stuck together to make up all the elements of the world around us. So tell us we went from there.

 

ErasmusErasmus : In the mid to late 1800s, showman/science lecturers would travel from town to town and demonstrate an early ancestor to the neon sign. They had a glass tube with wires at each end connected to high voltage.

When activated, the glass tube with glow with varying and different patterns of light. A neat showman’s trick for a non-technical non-scientific audience.

  • Julius Plücker, a German scientist and approximately 1859, improved the vacuum in his experimental glass bulb. He noticed that where the light originating from the cathode the glass it produced a fluorescent glow. He deduced that some sort of Ray, (cathode ray), was being created at the cathode and was responsible for the effect.

 

  • Jean Baptiste Perrin is the next scientist to contribute to a model of the world. He showed that the cathode Ray has negative charge. (Incidentally he also verified Albert Einstein’s explanation of the Brownian motion of microscopic particles suspended in liquids, thereby confirming the atomic/molecular nature of matter. He also explained that solar energy arose from the thermonuclear reactions embracing hydrogen.)

 

  • Emil Johann Wiechert a German scientist was the first to demonstrate that the cathode ray was composed of a particle stream. He correctly measured the mass to charge ratio of these particles which we now know to be approximately 1/1836 the mass of a corresponding atom such as a charged hydrogen atom. He failed to take the next step which was to conclude that these particles were a new elementary particle, which we now called the electron.


  • The German scientist, Philipp Eduard Anton von Lenard, was the 1st to show that these particles were able to travel through thin metal foil. This was perhaps the first inkling of the quantum nature of this particle. To us now, this would suggest concepts such as quantum tunnelling and the wavelike nature of the electrons originating from the cathode ray.


    Erasmus Erasmus:  The next advances were pioneered by the British physicist J.J.Thompson. There are three classical experiments attributed to scientist.

 

In the first experiment, Thompson built a cathode ray tube ending in a pair of metal cylinders with a slit between them. Behind the slit was an electrical device for catching and measuring electrical charge. Thomson was able to bend the cathode Ray with a magnet.

He was unable to separate the appearance of electrical charge from the presence of the cathode Ray. He concluded that the charge must be carried by elements will corpuscles within the cathode Ray. In future years, we came to know these corpuscles as electrons.
In the second experiment, Thompson overcame the failure of prior physicists to bend the cathode Ray with an electric field.

The behaviour of charged particles was understood well enough to know that a charged particle will be deflected by an electric field. This however had not been demonstrated by many experiments.

Thompson deduced that the charged particles within the cathode ray would not be deflected if they were surrounded by conducting medium, such as ionised gas within the experimental apparatus.

He methodically extracted the atmosphere from within the glass bulb, and was able to demonstrate that the electric field did in fact now deflect the cathode ray. He concluded the cathode rays are charges of negative electricity carried by particles of matter.

 



Thomson's apparatus in the second experiment Thomson Experiment 2 Thomson Experiment 2


In Thompson’s third experiment, he was able to measure how the cathode ray particles were bent by a magnetic field and to relate how much charge and energy they carried. He replicated this data using a number of tubes and a number of different gases.

This confirmed that the cathode rays were “general” constituents of many forms of matter. He also confirmed Emil Wiechert’s observation earlier that year that the mass to charge ratio of these cathode ray particles was of the order of 1/1836 the mass of a corresponding atom such as a charged hydrogen atom.

The conclusion was that these particles either were very light or carried an enormous electrical charge.

One of the tubes used in Thomson's third experiment.

Thomson Experiment 3 Thomson Experiment 3


His discovery is led Thompson to propose that the cathode ray is made up of a stream of particles or corpuscles, much smaller than atoms. He concluded that they were in fact pieces of atoms, in short subatomic particles. This contradicted a current view that atoms were not made up of smaller particles.

Most people thought that the atom was indivisible, and was the smallest component of matter. Initially Thompson’s experiments did not unambiguously support his conclusions, and in fact were met with scepticism by many of his colleagues.
KinkajouKinkajou : Ah, but eventually the truth wins out. We begin to enter subatomic and quantum world.
ErasmusErasmus :  The Irish physicist George Francis FitzGerald suggested in 1897 that Thomson’s corpuscles were free electrons. (This actually formed a disagreement with Thompson’s hypothesis. Fitzgerald believed that these particles existed in another state of matter,” the ether”).


Thompson subsequently proposed the “plum pudding “, or “raisin cake” model. In this he stated he believed that the thousands of tiny negatively charged corpuscles swarm inside a sort of massless positively charged cloud within the atom.
ErasmusErasmus :The next breakthrough was engendered by Ernest Rutherford. In 1911 he discovered that most of the mass of the atom resides within the nucleus. Rutherford and his assistant Hans Geiger developed a method of counting particles emitted by the radioactive decay of uranium or its associated chemical compounds.

They had noticed that a flash of light was emitted when a particle derived from radioactive decay of uranium heat a screen coated with zinc sulphide. If Rutherford’s theory was correct, the particles should be deflected less than a few degrees, (somewhat similar to a rifle bullet being deflected by heating a bag of sand). What they discovered was that approximately one in 20,000 particles were deflected by up to 90°. From this they concluded that most of the mass within the atom was concentrated in one very small area, (the nucleus).

By carefully measuring the deflections, Rutherford was able to conclude from his calculations that the radius of the nucleus of the atom is at least 10,000 times smaller than the radius of the atom. The majority of the volume of an atom therefore appeared to be empty space.


At this time Rutherford proposed the name proton for the positively charged particle residing in the nucleus of the atom. He also proposed the nucleus contained a neutral particle, eventually called the neutron. Confirmation of this proposed a particle took until 1932.

 

Rutherfords Laboratory Rutherfords Laboratory


At the same time that Rutherford proposed the name proton for the positively charged particle in the nucleus of an atom, he proposed that the nucleus also contained a neutral particle, eventually named the neutron.


In Germany, Walther Bothe and his student Herbert Becker had used polonium to bombard beryllium with alpha particles, producing a type of radiation. They hypothesised that this nuclear particle with no nuclear charge was a neutron. Chadwick followed up these results. He devised a simple apparatus that consisted of a cylinder containing a polonium source and beryllium target.

The resulting radiation could then be directed at a material such as paraffin wax; the displaced particles, which were protons, would go into a small ionisation chamber where they could be detected with an oscilloscope.  He was able to prove the existence of a particle with no charge in 1932.

KinkajouKinkajou : Wasn’t there are also a lot of work on the electromagnetic theory at this time? I think Maxwell’s equations belong to the ear of about 1870 to 1890.
ErasmusErasmus : True. Maxwell’s equations described the interrelationship of electric and magnetic fields. Fitzgerald was one of the 1st to suggest a device for producing rapidly variable electric fields to generate electromagnetic waves.

The German physicist Heinrich Hertz in 1888 showed this experimentally. Hertz was experimenting with a pair of Reiss spirals in 1886. He noticed that discharging electrical charge build-up in a Leyden jar into one of these coils would produce a spark in the other coil. In for the energy, namely electromagnetic energy was being transferred between the spirals.

He modified this experiment by using a Ruhmkorff coil (a type of transformer which changed low voltage DC input current into high voltage output current), to transfer an electric current to a 1 meter wire (effectively creating a half wave dipole antenna).

With a pair of these induction coils applying voltage to a pair of wires, sparks appeared across the gap between the wire ends, creating standing waves of radiofrequency current in the wires, radiating radio waves.

This experiment effectively produced radio waves and hundred megahertz range, roughly what we use today for TV transmissions. Further experiments prove the effects it was observing the results of Maxwell’s predicted electromagnetic waves.

 

Hertz Experiment
Hertz Experiment

 

By positioning the oscillator about 12 m from a zinc reflecting plate, he was able to produce standing waves whose magnitude, intensity, polarity and velocity could be measured. He found velocity of these ways was equal to the velocity of light. This imply that radio waves and light were all part of the electromagnetic spectrum
KinkajouKinkajou : It hardly seems possible to think that people did not realise that radio waves, visible light, ultraviolet radiation, and x-rays all were electromagnetic phenomena.  They were all a form of electromagnetic radiation obeying Maxwell equations.

Planck Experiment
Planck Experiment

ErasmusErasmus : the next advance came when Max Planck in 1900 presented theory that conjectured that energy was made up of individual units which are referred to as quanta. Planck had been working with black body radiators. A black body is a theoretical construct which completely absorbs all radiant energy input to it and after reaching an” equilibrium” temperature completely re-emits all this radiation. Blackbodies do not exist in nature.

However experimentally a good approximation can be obtained by using a closed box made of graphite or lamp black carbon walls with a small hole on one side allowing for observation of radiation emissions.

The box needs to be at uniform temperature, and be entirely opaque. Graphite forms a good approximation of a black body because it has an emissivity of greater than 95%.

Note that the (black) Rayleigh–Jeans curve never touches the Planck curve. The different colours represent different experiment temperatures.
Classical theory, predicts emissions along the) Rayleigh–Jeans curve. However this does not match measurements of the radiation frequencies observed at different temperatures.

To explain the differences between theoretical predictions and actual observations, Planck assumed that the sources of radiation are atoms in a state of oscillation and the vibrational energy of each atomic oscillator may have a series of discrete values (quanta), but never any value between.

  • By applying this discrete “quanta” approach, Planck was able to match the observed light emission spectra with new mathematical theory explaining the phenomena. He further extrapolated that the energy emitted must be proportional to the frequency of the atomic oscillator. This gave rise to what we now called” Planck Einstein relation”     
    E = hv (or Energy = h. freq; where h is the Planck constant.)
  • Planck’s constant states that the energy of each quantum is equal to the frequency of the radiation multiplied by the universal constant (6.626068 × 10-34 m2 kg / s).


    Black Body Radiation Black Body Radiation

ErasmusErasmus : In 1905, other scientists namely Rayleigh and Jeans as well as Einstein independently proved that classical electromagnetism could never account for the observed blackbody emission spectrum. These proofs are commonly referred to as the “ultraviolet catastrophe”.

The phrase refers to the fact that the Rayleigh-Jeans law accurately predicts emission ranges for frequencies below 105 GHz, but that there is a divergence of predictions and observations at electromagnetic radiation frequencies above 105 GHz (the ultraviolet range).


The inherent granularity in the appearance of radiation quanta appears counterintuitive to us in the macroscopic world. In this world it was possible to make things a little bit hotter or to make things move a little bit faster.

However because the quanta are very very small, the macroscopic human experience fails to appreciate the granularity of nature, making nature appears smooth to us.

ErasmusErasmus : The next development came with Niels Bohr refining the nuclear atomic model Rutherford by introducing quantised shell model in which electrons spin around the nucleus of the atom, in discreet layers. In this model Bohr proposed that electrons revolved in stable orbits around the atomic nucleus but can jump from one energy level to another energy level.

He proposed that when electrons dropped from a high energy level orbit to a lower one, they emit a quantum of discrete energy in the process, what we call a photon. This is the basis of what is now known as the “old quantum theory”.


The problem with the Rutherford model is that according to classical mechanics and electromagnetic theory any charged particle travelling on a curved path must emit electromagnetic radiation.

This is a by-product of Maxwell’s equations which predict that changing electromagnetic fields (such as the changing orbital vectors of an electron around and atomic nucleus), must emit radiation. Thus electrons must lose energy and spiral into the nucleus. This suggests that the Rutherford model of the atom is not stable and contravenes observations. (Atoms are stable).

  • Bohr developed the Bohr model of the atom, in which he proposed that energy levels of electrons are discrete and that the electrons revolve in stable orbits around the atomic nucleus but can jump from one energy level (or orbit) to another. Although the Bohr model has been supplanted by other models, its underlying principles remain valid.

Bohr's starting point was to realize that classical mechanics by itself could never explain the atom's stability. A stable atom has a certain size so that any equation describing it must contain some fundamental constant or combination of constants with a dimension of length.

The classical fundamental constants - - namely, the charges and the masses of the electron and the nucleus - - cannot be combined to make a length. Bohr noticed, however, that the quantum constant formulated by the German physicist Max Planck has dimensions which, when combined with the mass and charge of the electron, produce a measure of length.

Numerically, the measure is close to the known size of atoms. This encouraged Bohr to use Planck's constant in searching for a theory of the atom.

Bohr Atom Simple Bohr Atom Simple
Using Planck's constant, Bohr obtained an accurate formula for the energy levels of the hydrogen atom. He postulated that the angular momentum of the electron is quantized--i.e., it can have only discrete values.

He assumed that otherwise electrons obey the laws of classical mechanics by traveling around the nucleus in circular orbits. Because of the quantization, the electron orbits have fixed sizes and energies. The orbits are labelled by an integer, the quantum number n.

The Addition of Spin

It was mentioned earlier that another new idea is needed before the classical physics of electrons and nuclei properly turns into chemistry. That idea is spin, a third property of electrons and nuclei alongside mass and electrical charge.

Paul Dirac showed that spin is a natural property of charged particles within quantum mechanics. Wolfgang Pauli showed that the spin of the electron prevents more than one electron occupying the same state at the same time-the Exclusion Principle-a fact responsible for the whole of chemistry.

He felt that quantum mechanics with spin seems to account for pretty much all the world seen around us.

 


ErasmusErasmus :   in 1905 Albert Einstein theorised that there is equivalence between mass and energy.  To understand his theory we will first consider a particle of light electromagnetic radiation, generally known as a photon. Photons are known to have energy and to have momentum.

However they do not appear to have any mass. James clerk Maxwell established this first in the 1850s. However, we know that momentum is made of the two components mass and velocity. So photon has momentum it must have a mass.


Einstein proposed that we imagine a stationary box floating in deep space. Within the boundaries of the box, a photon is emitted and travels from left to right. The box must recoil to the left as the photon is emitted, for the momentum of the system to be conserved.

When the photon collides with the other side of the box it transfers all its momentum to the box. The total momentum of the system is conserved so the impact quarters the box to become stationary again, i.e. to stop moving.


However, as there are no external forces acting on the system the centre of mass of the box must stay in the same location. But the box has moved. Einstein resolve this conundrum by proposing that there must be a mass equivalent related to the energy of the photon.

By converting the energy of the photon into mass, it allows the centre of mass of the system to be conserved.


This becomes a proof that there is relationship between mass and energy.

On this basis he derived the mathematical formula we now know as E=mc2, though initially it was presented differently.

  • In December 1907, Einstein expressed the equivalence in the form M = μ + E0/c2 and concluded: A mass μ is equivalent, as regards inertia, to a quantity of energy μc2. [...] It appears far more natural to consider every inertial mass as a store of energy

ErasmusErasmus : The next advance was made in 1923 by Louis DeBroglie. He used the work of Einstein to derive a relationship between momentum and the wavelength of light.

Initially Einstein in his theory of “special relativity” proposed two equations:
E=mc2   and E = hv

DeBroglie combined equations to arrive at   De Broglie Equation
The de Broglie wavelength is the wavelength, λ, associated with a particle and is related to its momentum, p, through the Planck constant, h:
For a particle of zero rest mass such as a photon, DeBroglie knew that Energy Momentum Equation

(Here p=mc= momentum. So mc=E/c: rearranging gives the familiar mc2 =  E
:
so we all know this one)

 

 

For a photon, he also knew form the work of his predecessors that
where E=pc (E: energy, p: momentum, c: speed of light).
This then gives the DeBroglie formula De Broglie Wavelength > De Broglie Wavelength

Although DeBroglie derives momentum wavelength relationship for photons, in 1924 in his PhD thesis, he hypothesised that this relationship can be adopted to describe matter such as electrons, protons or neutrons as well.


To understand where the future takes us, we need to understand some other scientific principles. Previous researchers have demonstrated that the regular periodic recurrent crystal structure serves a type of three-dimensional diffraction grating.

Mathematical rules were developed to measure the angles of maximum reflection for constructive interference from three dimensional arrays, such as found in a crystalline lattice.

The wavelike nature of x-rays had been demonstrated through x-ray scattering experiments on crystalline solids lattices. It was expected that only wavelike materials can be diffracted by crystalline lattice.

ErasmusErasmus :  It took three years until there was an experiment undertaken to assess the reflection of electrons from a crystalline lattice. Expecting reflection The Davisson Germer experiment observed diffraction. It revealed that matter can behave in ways that are wavelike.


Davisson and Germer intended to study the surface of a piece of nickel directing an electron beam at the surface and observing how many electrons bounced off at various angles .

A specially designed faraday cup electron detector moved on an arc path around the nickel target, and was designed to detect only elastically scattered electrons. In accident during experimental process, air into the chamber and oxidise the surface of the nickel target.

Davisson and Germer attempted to remove the oxide by heating the nickel. Inadvertently, this changed the formerly polycrystalline structure of the nickel to form a large single crystal area with crystal planes continuous over the width of the incident electron beam.

They had regularised the surface of the nickel crystal and created a regular crystalline lattice capable of deflecting incident wavelike particles.

They had expected that because the electrons they were using were very small particles, even the smoothest crystal surface would be too rough and would create reflections of the incident electron beam.

Davisson Germer Experiment Davisson Germer Experiment


When they started the experiment again at Bell laboratories in 1927, the electrons hit the surface, and they were scattered by atoms which originated from crystal planes inside the nickel crystal.

They generated a diffraction pattern with unexpected peaks. Davisson and Germer's accidental discovery of the diffraction of electrons was the first direct evidence confirming de Broglie's hypothesis that particles can have wave properties as well.


This experiment forms one of the tenants of quantum theory, showing the wave nature of matter and demonstrating that matter may have wave particle duality.

 
The experiment not only played a major role in verifying the de Broglie hypothesis and demonstrated the wave-particle duality, but also was an important historical development in the establishment of quantum mechanics and of the Schrödinger equation.

ErasmusErasmus : The next development in quantum theory followed Werner Heisenberg’s development of the uncertainty principle. The uncertainty principle was a theoretical concept extrapolated from the work of others.

Basically it states that the position and momentum of a particle cannot be simultaneously measured with arbitrarily high precision. There is a minimum uncertainty with the measurement either of position or momentum related to the Planck constant. The uncertainty principle arises from the wave properties inherent in the quantum constituents of matter.

Even with perfect instruments and technique, uncertainty is inherent due to the structure of matter.

When you describe an electron is having a wavelike nature, this implies that the electron wave is a quantum mechanical wave function and that there is a “probability” of finding an electron at any point in space.
p= is a reiteration of DeBroglie’s formula.


(To explain as simply as I can, we can substitute 1/ Δx for wavelength λ as Δx represents the width of a diffraction grill defining the position of the particle. This position varies inversely with the wavelength.

Simply, a longer wavelength has a proportionately lower probability of appearing at a specific point on that wavelength: as for example being present as a particle at a particular point or width Δx as represented by the width of the diffraction grille gap. Big wavelengths, lower probability of being at one bit of that wavelength position wise).


(The proofs especially in 3D are a lot more complex but are probably beyond the mathematical skills of many of us, so I’ve chosen to stick to simple).
If we substitute Δp (representing uncertainty) for the measurement of momentum,
and if we substitute 1/Δx (representing uncertainty in the measurement of position) for the wavelength, we get Δp=h/Δx.

Werner Heisenberg
Werner Heisenberg


Werner Heisenberg rearranged this formula to give, the expression with meaning: The range of error in position (x) times the range of error in momentum (p) is about equal to or greater than the Planck constant.

Uncertainty Principle
 This is perhaps the most famous equation next to E=mc2 in physics.

A consequence of this theory is the development of the principle of “complementarity”. This implies that is impossible to sharply separate the behaviour of atomic or subatomic objects from their interaction with measuring instruments. If you measure momentum you cannot measure position.

If you measure position you cannot measure momentum. The combination of position, energy (momentum) and time are actually undefined for a quantum particle until a measurement is made (WE describe this situation as the wave function for the particle collapsing).


Because Planck’s constant his so small (of the order of 10-34), the uncertainty principle is not significant in our assessment of the position to large scale (polyatomic) objects which are substantially larger than subatomic particles.

If we use some of this maths, we can work out the energy required to “contain” an electron for example within an atom or an atomic nucleus. (p=momentum, Δp for our purposes)

Bohmian Mechanics Bohmian Mechanics


E= mc2  for mass and energy equivalence and E= 1/2 mv2 for kinetic energy     >>   
or for Kinetic Energy          E= (mc) 2 /2m    >> or        E=p2 / 2m  
These two are not related equations. In the first equation E = m.c^2 the equivalence of mass and energy is stated. 
In the second equation E = 1/2 m.v^2 the relationship between the kinetic energy and velocity of a mass m is stated.


Δp=h/Δx. So calculating,
Assume atomic size is 0.4 nm Δp=h/Δx = 6.6261.E-34 J.s/ 4.E-10 m=1.6565.E-24 J.s/m
or        E=p2 / 2m    = (1.6565.E-24) /   2 / 9.11.E-31 kg/1.60 J/ev conversion factor
gives 9.4 ev (electron volts)


So calculating Energy gives:

  • Assume atomic size is 0.4 nm 9.40 ev (electron volts) to retain electron within the atom
  • Assume Nuclear size is 1/20 000 of 0.4 nm = 9.4* 400e6 / 1 e9 GeV=3.76 GeV
    to retain electron within the nucleus of the atom =  3.76 GeV
  • Assume Proton mass is 1836 * Electron Mass= 3.76 /1836 * 1000 Mev = 2.05 Mev
  • to retain the proton within the nucleus of the atom = 2.05 Mev

KinkajouKinkajou : So why we digressing into atomic structures?


ErasmusErasmus : When we start talking about astronomical phenomena, the numbers start becoming useful. The suns of our universe literally form a giant laboratory of subatomic reactions at macroscopic scales. Explanations and theories become important.

Big Bang and MatterNature of Matter in Universe Nature of Matter in Universe

Dark Matter Dark Matter

NonBaryonic Matter NonBaryonic Matter

Non Baryonic Matter
Non Baryonic Matter

 

 

Baryons Baryons

Baryonic Matter Baryonic Matter

 

 

Any other examples we can see that having Planck’s constant within the formula determines the size of the confinement that can be produced by the fundamental forces of electromagnetism or from strong nuclear forces. In short this constant determines the size of atoms and their nuclei.

When we consider objects such as electrons in very small “orbits” for example such as around an atomic nucleus, the only possible orbital states must been exact multiple of the Planck’s constant. Crudely put this mechanism explains why atoms can only shrink to a certain point and still remain stable.

 

Advanced Bohr Atom
Advanced Bohr Atom

 


According to de Broglie the electron is described by a wave and a whole number of wavelengths must fit along the circumference of the electron's orbit: This approach essentially confined the electron wave in one dimension, along a circular orbit of radius r.

KinkajouKinkajou : So were finally starting to reach the time of the modern era. Who’s next in the physics in Hall of Fame?
ErasmusErasmus : A scientist called Schrödinger, invites us to the discussion next. I think we’ll talk about the history, because it’s a bit easier to understand the mathematics.

After discussions with his colleagues, Schrodinger decided to develop a proper three-dimensional wave equation for the electron. Others have a ready attempted this task (e.g. Heisenberg’s matrix mechanics, the De Broglie–Bohm  theory proposed a real valued wave function connected to the complex wave function by a proportionality constant), but their solutions had not been accepted. 

Schrödinger’s working proposition was that if particles behave as waves, they should satisfy some sort of wave equation. In in December 1925, Schrodinger secluded himself away in isolated mountain cabin to consider. The non-relativistic version of the wave equation he developed showed the correct solutions for the spectral energy is of hydrogen, which he published in a paper in 1926.

Showing a solution calculate the hydrogen spectral series by treating the hydrogen atoms electron as a wave Ψ(xt). This weight moved in a potential energy well created by the proton in the nucleus of the hydrogen atom. 1926 paper was supported by Einstein who saw concept of matter waves as a more intuitive depiction of nature compared to other theory such as Heisenberg’s matrix mechanics.


It remained to other physicists, notably Max Bohm to extend the theory of matter waves. Bohm interpreted Ψ as the probability amplitude of the matter waves whose absolute square is equal to the probability density.

Schrödinger’s treatment of matter as a wave function redefine quantum world. Matter can essentially exist in an infinite number of places at any given time. Things can disappear in one place and reappear somewhere else. It is not possible to simultaneously know the exact position and momentum of an object.

It proposed a method to explain the concept of quantum entanglement. If to mirror the particles are separated and undergo a quantum evaluation experiment, entanglement means that a change in one particle is instantly reflected in its counterpart.


The Schrödinger equation is not the only way to make predictions in quantum mechanics - other formulations can be used, such as Werner Heisenberg's matrix mechanics, and Richard Feynman's path integral formulation.

Schrödinger is perhaps most famously remembered for his thought experiments such the famous “Schrödinger’s cat” model. In this experiment Schroeder placed an imaginary quantum cat in a sealed box.

The quantum cat faces a gun, which is triggered by Geiger counter tuned to a piece of uranium. The uranium is unstable and undergoes radioactive decay. If the uranium nucleus disintegrates, is detected by the Geiger counter, which then triggers the gun, whose bullet will kill the cat. In the Schrödinger experiment, to decide whether the cat is dead or alive, we must open the box and observe the quantum cat.

However what is state of the quantum cat before we open the box? The answer according to quantum theory, is that the cat is described by wave function that describes the sum of a dead quantum cat and alive quantum cat.

Schrondingers Cat
Schrondingers Cat


Schrödinger’s thought theory demonstrates the conflict that appears in reconciling what we intuitively believe to be true, and what our theories tell us about the world in which we live.


Since we cannot know, according to quantum law, the cat is both dead and alive, in what is called a superposition of states. It is only when we break open the box and learn the condition of the cat that the superposition is lost, and the cat becomes one or the other (dead or alive).

This situation is at times called quantum indeterminacy or the observer's paradox. The paradox is that: the observation or measurement itself affects an outcome, so that the outcome as such does not exist unless the measurement is made. (That is, there is no single outcome unless it is observed.)

Cat Paradox Schrodinger

Cat Paradox Schrodinger


Schrödinger is reputed to have related later in life, that he wished he had never met that cat.

Double Slit Electron Experiment Double Slit Electron Experiment

Problem most famous experiment demonstrating the concept of matter waves is the double slit experiment showing the accumulation of electrons after passing through two slit gaps in a target screen. In this experiment a single electron particle is fired through a double slit, one at a time.

There is only a single electron passing through the screen at one time therefore under classical theory there should be a scattering of dots visible not an interference pattern.

However the experiment reveals that an interference pattern is recorded. The conclusion is that the electron must passed through both slits at the same time thereby interfering with its own wave function, creating an interference pattern which is observed and experiment.

Two Slit Electron Experiment Two Slit Electron Experiment


The same result can be observed by moving water waves through double slit barrier, resulting in an interference pattern on the other side of the barrier.


So the concepts demonstrate by quantum theory at this time are: diffraction of particles (showing their wave like properties), interference of matter waves (showing the wavelike properties of electrons) and superimposition (see is whereby the matter waves originating from single electron probabilistically superimposed on each other creating the observed interference pattern).

Two Slit Experiment Particle waves Two Slit Experiment Particle waves