### Quantum Mechanics for Dummies

I have been requested to produce an article on quantum mechanics which is accessible to the interested lay person, and so I oblige. To begin with, let's run through a brief history of quantum mechanics. The first evidence that could not be explained by Newtonian physics were the solar spectral lines. In 1814 Joseph von Fraunhofer noticed a number of dark lines in the solar spectrum (produced by sending sunlight through a prism or a diffraction grating). He gave each line a name such as C (produced by hydrogen) or D1 (produced by sodium) but he could produce no physical explanation for these dark lines. Each line represents reduced energy being emitted by the sun at a specific wavelength. These solar spectral lines were soon discovered in the light emitted by other stars but they remained totally unexplained for almost a century.

In 1900 the German physicist Max Planck hypothesized that the quanta (i.e., individual packets of energy) released by a hot object could best be explained if they had discrete energy values. He proposed the now-famous Planck equation:

E = n * h * nu

where E is the energy of the quantum, n is a postive integer (e.g., 1, 2, 3, etc.), h is the famous Planck's constant (6.626E-34 joule-seconds), and nu is the frequency of the light in Hertz (cycles per second). Thus, an individual photon (i.e., quantum) of light can have an energy of h*nu, 2*h*nu, 3*h*nu, etc. but not 1.5*h*nu, 2.1*h*nu, etc. The energy of the photon is said to be quantized and the new branch of physics introduced was called quantum mechanics (based upon the classification of the old branch of physics as classical mechanics or Newtonian mechanics).

In 1905 (the same year that he published his Special Theory of Relativity) Albert Einstein presented evidence that the photoelectric effect (i.e., the ejection of electrons from atoms via light) involved discrete particles of light which he named photons. The photons were the same as Planck's quanta.

In 1913 Niels Bohr showed how the new quantum theory could explain the solar spectral lines which had puzzled Fraunhofer almost a century before. Bohr constructed a quantum model of the hydrogen atom which still has explanatory power even today. In the Bohr atomic model the electrons orbit the nucleus (i.e., a single proton for hydrogen) in discrete circular orbits. The lowest orbit has quantum number N = 1, the second lowest orbit has quantum number N = 2, and so forth. The higher the N number the greater the energy the electron possesses. When an electron falls from a higher orbit to a lower orbit it produces a photon of light whose energy is the energy difference in the orbits. An electron can climb to a higher energy orbit by absorbing a photon whose energy equals the energy difference in the orbits. Thus, the Bohr model could explain discrete energies (i.e., wavelengths) for emitted or absorbed light and thus the solar spectral lines.

Bohr also postulated what he called the Correspondence Principle which said that in the limit as N goes to infinity the predictions of quantum theory and classical theory must agree. Thus, classical physics is nothing but a derivation of quantum physics for large quantum numbers. Planck, Einstein, and Bohr produced what is known as the Old Quantum Mechanics which was a complete theory by the year 1915. But it was soon to be eclipsed by the New Quantum Mechanics in a few short years. I will have more to say about the New Quantum Mechanics in a future post.