IIA. History of the Discovery of Quantum Mechanics.

We will describe how a search for a mathematical description of nature led to an unanticipated theory, a theory that pertains to a world completely unlike that of our everyday concepts.  To the pioneering physicists of the period from 1900 to 1926, obtaining a unified mathematical description of nature became more important than sticking with conventional concepts.  Note: Classical physics is the highly successful Newtonian form of physics used from 1700 to 1900.

1. Thermal Radiation.  Planck, 1900

Thermal radiation is the radiation emitted in the form of infrared and light waves by a hot object, like the filament in a light bulb.  Planck first found the correct equation—the one that accurately fit all the data—by an educated trial and error process.  He then derived this equation by assuming the energy of light was quantized.  It could only take on the values hf, 2hf, 3hf and so on (instead of a continuum of values), with f being  the frequency (number of times the wave oscillates per second) and h being a new constant of nature, now called Planck’s constant.

2. The Photoelectric Effect.  Einstein, 1905

If ultraviolet light is shone on a piece of metal, electrons are splashed out of the metal.  Einstein obtained an equation that agreed accurately with the measured results by building on Planck’s results.  He assumed that, embedded within a light ray are particles of light, now called photons, which have energy hf.  Even though it satisfactorily explained the data, Einstein’s particle hypothesis was viewed skeptically at the time because light was strictly a wave in the very successful classical theory of light.

3. The Compton Effect.  Scattering of Light by Electrons.  Compton, 1922

If x-rays are bounced off electrons, they are changed in frequency and direction.  The results can be accurately explained if one assumes x-rays (which are very short “light” waves) consist of particles embedded within a wave.  Thus Einstein’s photon hypothesis was vindicated.

4. Rutherford Scattering and the Structure of the Atom.  Rutherford, 1910

The structure of the atom was not known in 1910.  Rutherford, in the first scattering experiment, bounced helium nuclei (alpha particles from a radioactive source) off gold atoms.  The results showed there was a very small, positively charged nucleus at the core of the atom.  This greatly puzzled physicists because there was no way in classical physics to make an electrically stable atom with all the positive charge concentrated at its center.

5. The Bohr Atom. Bohr, 1913

The primary puzzle at the turn of the century was why hydrogen emitted a discrete spectrum of light—consisting of just a few colors—rather than a continuous rainbow-like spectrum.  Bohr found that he could exactly explain the discrete spectrum if he assumed the following picture: The hydrogen atom consisted of a point charge in the middle and a point electron orbiting around it.  The electron was assumed, without justification, to have a stable orbit if and only if the radius of its orbit satisfied a certain condition (involving Planck’s constant; such an interlock of ideas!)  There were perhaps two dozen different colors of light that could be observed coming from hydrogen, each with its own characteristic color or wavelength (the distance between peaks in the wave).  Bohr’s model of the atom gave the correct values for all these wavelengths to one part in a million. 

This is what physics does.  It assumes a certain conceptual picture of physical reality, derives equations from that picture and compares them to experiment.  Perhaps 95% of all the conceptual pictures that physicists try lead to wrong results.  These are expunged from the pages of history.

6. de Broglie’s Waves. de Broglie, 1923

de Broglie took Einstein’s idea of the association of a particle with a wave (in the case of light) and applied it in reverse.  He assumed there was a wave associated with the particulate electron in the hydrogen atom.  He applied a geometrical condition to the wave of the orbiting electron (it had to properly meet itself after going around the circle) and thereby partially justified Bohr’s hypothesis on the condition for a stable orbit.

7. The Schrödinger Equation.  Schrödinger, 1926

Finally, Erwin Schrödinger thought that if there was a wave associated with the electron, it must obey some equation.  Using certain heuristic ideas, he derived the equation, which is now known as the Schrödinger equation.  This equation gave the correct values for the wavelengths of light emitted by the hydrogen atom, and fully explained the stability of the atom.

But in Schrödinger’s theory, the idea of a stable orbit has lost its meaning because there are no longer particles in the mathematics.  Instead his equation is for the wave function (section IIA4).  This can be pictured as a spread out “mist,” as if the electron were spread out instead of being a point particle.  It turns out, however, that, although useful, this is not a fully valid picture.  And in fact, it is difficult to obtain a simple conceptual understanding of the wave function in terms of everyday concepts.

The point is that, through all these steps—Planck’s quantization of energy, Einstein and Compton’s association of a particle with a wave, de Broglie’s association of a wave with a particle, and finally, Schrödinger’s equation for the wave—a comfortable, familiar view of the physical world was sacrificed to find mathematical equations that matched the experimental results.  Mathematics, rather than one’s everyday concepts, rules in the attempt to find the true nature of physical existence.

Note: Even though the concept of a particle was used above, we will show in section IIB that there is actually no evidence for the existence of particles such as electrons, photons and atoms.