Max Planck, quoted in Walter Moore’s SCHRODINGER: Life And Thought, once said that Erwin Schrodinger was the man who worked out this idea “that an electron moving with a certain velocity behaves in many respects like a wave of definite period and transmission velocity.” That is as pithy of a summary of Schrodinger’s Wave Theory as one is likely to find.
Before Schrodinger even contemplated applying wave theory to electron behavior, he had already written papers on sound dampening as a function of altitude and on color theory (specifically on the four basic colors theory versus the three basic colors theory [last I heard, both turned out to be right, depending on if one is discussing color in the eye or color in the brain]).
Moore does not go much into Schrodinger’s sound-dampening work, but he does say that it was known that the shorter the sound’s wavelength, the greater the dampening, or attenuation, of the sound, and that the higher altitude, the more sound damping there is. My bet is that this is simply due to the fact that, in each case (smaller soundwaves and higher altitudes) less air molecules are being “hit” by the travelling sound wave to continue transferring the wave soundly (pardon the pun)– as in, without loosing wave integrity. But that’s just a guess, and neither here nor there for the direction I want to take today’s story…
Also occurring before Schrodinger came up with his wave theory was the revolution in physics that occurred during the seventeen and eighteen hundreds when the behavior of gases was absorbing a lot of study and talent. This is when the statistical nature of physical events begins coming into play.
For example, imagine pumping a gas into an empty room. One cannot predict the precise path that each and every individual gas molecule will travel, but one can predict that the gas molecules will eventually evenly distribute themselves over the entire room due to the effects of impact, recoil, and inertia; in other words, they will stop going in the direction in which they slam up against another gas or wall molecule, but will keep going in the direction in which they don’t. Thus, we can only speak statistically about the (very high) probability that the group of gas molecules will spread out, but not about the path of one individual molecule.
Quantum Theory will take the statistical/probability ball and streak naked down the highway with it.
Another pre-Wave-Theory thread running through the Schrodinger story is the work done by De Broglie which was the inspiration and the actual first steps toward a Wave Theory of Matter. De Broglie contended that particles are guided through space by trains of waves, sometimes called Pilot Waves. He used his theory to predict the wave-frequency of a moving electron.
Using De Broglie’s work as his springboard, Schrodinger began coming up with his own theory of the wave nature of matter. De Broglie’s waves travel through space, pushing along particles. But Schrodinger’s waves are “standing waves”– waves which maintain their general position, like the vibration of a plucked guitar string. And they do not push along Matter; Schrodinger’s waves, in essence, are the Matter.
Schrodinger’s first attempt at a standing wave theory, the only one I know of in which he accounted for the requisites of Einstein’s Relativity Theory, failed to describe Electron behavior adequately because it neglected to account for Electron Spin.
Later, in 1926, Schrodinger was able to produce a paper which did, indeed, account for the correct energy levels of the Hydrogen atom– though this work does not try to tackle Relativity considerations.
Schrodinger believed that his theory explained the quantized nature of the energy patterns of Hydrogen “in the same natural way as the integers specifying the number of nodes in a vibrating string.”
Schrodinger, says Moore, imagined the atom “to be vibrating with a potpourri of very high frequencies.” It is between these vibrational frequencies that atoms release or absorb energy.
Thus, instead of “quantum leaps,” in which Electrons are said to instantly transport from one atomic orbit to another without actually ever travelling in between the two orbits (as if by magic!), in Schrodinger’s theory the different frequencies of the Electron are different vibrations of the negative charge surrounding the atom.
Schrodinger never really believed much in quantum jumps. He felt his Wave Theory explanation of Electron behavior made much more sense than “today’s doubtful reality of the Electron orbits.” Instead of single points of negative charge, Schrodinger imagined Standing Waves filling the entire Electron path at once, and even extending far beyond it. “No special meaning is to be attached to the Electron path itself,” he said, “and still less to the position of an Electron in its path.”
However, Schrodinger’s Wave Theory had plenty of its own detractors, and in fact, the quantum leap school of thought was never really in jeopardy of losing its position as the orthodox interpretation of atomic events (though, Schrodinger did have some big-name scientists on his side, including Einstein).
Schrodinger, says Moore, believed that waves, not particles, constituted “the basic reality of the subatomic world.” He saw particles as being comprised of a group of waves travelling together. He called these groups of waves making-up particles “wave packets,” and said that a particle “corresponds to that point where a certain continuum of wave forms coalesces with the same phase.” The particle (or rather, the Wave Packet that is the particle), then “moves with the group velocity of the wave packet.”
Schrodinger at first held literally to his idea of Particle-As-Wave-Packet, thinking of all matter as wave disturbances in space.
One of Schrodinger’s sharpest critics was Lorentz. Lorentz pointed out that a packet of waves travelling through space would soon disperse, and thus could not very well maintain the form of a tiny particle.
Specifically, Lorentz said that the area of the Electron energy around the Hydrogen atom was not large enough to sustain a wave packet, since to persist for any length of time a Wave Packet would need a very large range compared to its wavelength– a domain larger than the little Hydrogen atom could provide. Or, said another way, Lorentz objected that the Hydrogen atom cannot offer the wavelength vibrations short enough for wave packet construction.
An objection of Lorentz that I wasn’t fully clear about was this: according to Moore, Lorentz objected that Schrodinger did not include the Electron field in his wave function (!?). I’ve never hard this objection before, and find it difficult to believe that this would be something Schrodinger could just feel good about leaving out, but Schrodinger is said to have countered that, since his theory did away with the necessity of having an actual Electron particle revolving around a nucleus, that one “can be readily satisfied that only the term for the nuclear charge appears.” This was all over my head, but I thought it important to point out, especially if I have interpreted it correctly.
Moore also states in his book that Schrodinger’s Wave Theory never actually determined the exact frequencies of light absorption by atoms, but that Schrodinger merely suggested that the precise frequencies would be some combination of the frequencies of the vibrations predicted by his theory. Again, I have never heard this objection, and I am struck by how little, serious, point by point critique of Wave Theory I’ve come across in my studies up til now.
After such objections, Moore says that Schrodinger “soon de-emphasized the wave-packet picture.” He began instead to re-interpret his theory, focusing less on the fundamental nature of matter and more on what his theory said about the density of the “smeared-out” Electron charge in an atom.