Quantum Fuzz
Pauli in 1925 postulated “exclusion”, that no two electrons would be able to occupy the same overall state. That is no two electrons would have the same set of quantum numbers n, l, m and spin. [Again Pauli did this without proof or physical reason, except that it fit the arrangement of the elements in the periodic table.] The electrons in an atom would populate the available states, one electron per state, starting with the lowest-energy states. Once every state in a shell had one electron in it, the next electron would go on to start the occupation of the lowest-energy state in the next, higher-energy shell. The last, highest-energy, occupied electron state in any atom would register the degree to which that atom’s outermost shell was filled. The chemical properties of that atom, that element, would be in large measure determined by the closeness to which the electrons came to completing the full occupancy of a shell: for instance, two states away, one state away, full occupancy [a noble gas], one more than full occupancy, and so on. It worked, and he earned a Nobel prize in 1945 for: the discovery of the Exclusion Principle, also called the Pauli Principle.
Arthur Compton, at the University of Wisconsin over the winter of 1922-1923, found an extraordinary result while working with x-rays [high-energy electromagnetic radiation with wavelengths approximately the sizes of atoms]. Monochromatic x-rays shining on graphite reflected back with changed and lengthened wavelengths. It was as if violet light reflecting off of a substance would change its color to red in the process. What was observed is now called the Compton Effect. What was seen couldn’t be explained by waves at all. The Only viable explanation was that the electromagnetic radiation, as Einstein had shown theoretically in 1916, had momentum in the same sense that a particle has momentum.
Louis de Broglie pictured the electrons in Bohr’s orbits as being related to standing waves, like the harmonic vibrations in a guitar string. [These are standing because they are trapped and don’t go anywhere.] The half-wavelength string would vibrate up and down at the string’s “fundamental” frequency, determining the string’s basic pitch. These extremes mark the “amplitude” of the vibration. The three “harmonics” contribute to the timbre of the string’s sound. These harmonics vibrate at successive integral multiples of the fundamental frequency.
Classical ideas, classical physics, can in no way explain the wave nature of individual particles. The double-slit experiment, either for single electrons or for single light quanta, remains one of the best demonstrations that proves we live in a quantum world. And our quantum world is strange, QM provides an explanation for this strangeness.
Wave Mechanics and Schrodinger’s Wave Equation: James Watson refers to Schrodinger’s book What is Life, written in 1944, as having inspired Watson, Crick, Wilkins, and Franklin to discover the double-helix structure of DNA. Published March 1926, Schrodinger’s wave mechanics was welcomed by Bohr and Einstein and eventually most in the field; it was challenged especially by Heisenberg, who was increasingly becoming frustrated that the physics community was endorsing Schrodinger’s concepts rather than his own. During Schrodinger’s lecture in Munich, Heisenberg asked questions that Schrodinger had difficulty answering. For example, he could not explain the photoelectric effect: How could the electron emerge as a “popped loose wave”? And how would a wave carry the charge of the electron? Schrodinger at first thought this could be done with the charge smeared-out in some fashion. But this would seem to deny the electron’s observed particle nature and possession always of a single, indivisible localized basic unit of charge. Following the meeting, Bohr invited Schrodinger for a visit to Copenhagen. In October, the two of them, together with Heisenberg, would try over several days to sort out conflicts and questions in both theories. Dirac was able to show that matrix and wave mechanics were just special mathematical cases of his own “transformation theory”.
