Wave Mechanics 193
results. He was greatly discouraged and depressed and dropped the
whole project for a number of months. When he returned to his work
he realized that if he dropped the relativistic equation and ignored
relativistic effects due to the electron’s motion that a non-relativistic
reversion of his original equation produced the desired results.
Schrödinger’s equation is a non-relativistic equation. Relativistic
corrections to his equation were developed later by Dirac who discovered
the source of Schrödinger’s original problems. Schrödinger encountered
difficulties because he had attempted to make two steps at one time. This
rarely happens in physics. Progress is usually made one step at a time.
Schrödinger developed de Broglie’s idea, who in turn, had developed
Einstein’s idea, who, in turn had developed Planck’s idea.
De Broglie’s standing wave formalism only allowed him to reproduce
the Bohr frequency condition. Schrödinger’s equation allowed him to
calculate the exact energy of the atomic levels. Because his equation
included the effects of the electromagnetic potential on the electron, he
was also able to derive the corrections to the Bohr levels due to an
external magnetic field (Zeeman effect) or due to an external electric
field (Stark effect).
In addition to giving excellent agreement with spectral data
Schrödinger’s results helped to explain the nature of the electron’s
behaviour in the atom. Instead of the picture of the electron jumping
discontinuously from one quantum state to another, a new view
developed. An atomic transition from one level to another was seen as a
transition from one standing wave configuration to another. The image of
the standing wave also helped to explain why the orbits were quasi-stable
and why only certain orbits were allowed.
As with any other new development in physics, Schrödinger’s results
provided the solution to a number of problems but only at the price
of raising new problems. The foremost question was the interpretation
of the standing waves. What were they in fact waves of? Schrödinger
at first considered the electron literally as a material wave whose
dimensions were given by that of the standing wave. It became apparent,
however, that the standing wave represented a cloud of probability. That
the actual dimensions of the electron were quite small and that only
its probability of being detected was spread out through space. These
probability standing waves that are spread out over space do not
represent the electron spread out over space rather they represent the
probability amplitude of finding an electron, which when found is just