Wavepackets and the Principle of Superposition
To return momentarily to the electron traveling through a vacuum, it is clear
physically that it must have a wave function that goes to zero far away in either
direction (well still work in one dimension, for
Bohrs Semiclassical Argument to Fix the Quantum of Angular Momentum
However, Bohr found a clever theoretical way to determine RH from his model: by
equating his prediction of the frequency emitted when an electron goes from one orbit
to another in a very
Schrdinger believed the above continuity equations represented the conservation of
electric charge, and had no further significance. He thought that after all his own
equation showed the electron to be just a smooth classical wave at the deepest
level. In
What does the Wave Equation tell us about the Photon?
We know from the photoelectric effect and Compton scattering that the photon energy
and momentum are related to the frequency and wavelength of the light by
Notice, then, that the wave equation tells u
Schrdingers Equation for a Particle in a Potential
Let us consider first the one-dimensional situation of a particle going in the xdirection subject to a roller coaster potential. What do we expect the wave function
to look like? We would expect the wavel
A Nonrelativistic Wave Equation
Continuing along the same lines, let us assume that a nonrelativistic electron in free
space (no potentials, so no forces) is described by a plane wave:
.
We need to construct a wave equation operator which, applied to this
The Nature of Light
It is firmly established experimentally that the propagation of light is well described
by a wave equation, which in fact is not difficult to derive from Maxwells equations:
.
For a plane wave moving in the x-direction this reduces to
A Challenge to Schrdinger
De Broglies doctoral thesis, defended at the end of 1924, created a lot of excitement
in European physics circles. Shortly after it was published in the fall of 1925 Pieter
Debye, a theorist in Zurich, suggested to Erwin Schrding
The Nature of Matter
By the 1890s and early 1900s, most scientists believed in the existence of
atoms. Not allthe distinguished German chemist Ostwald didnt, for example. But
nobody had a clear picture of even a hydrogen atom. The electron had just been
d
Localizing an Electron
It is necessary to think a little more carefully about the wave function corresponding
to an electron traveling through a cathode ray tube, say. The electron leaves the
cathode, shoots through the vacuum, and impinges on the screen.
Remark: the Bohr Atom is Still Important!
Although, as we shall see shortly, Bohrs semiclassical analysis has long been
replaced by Schrdingers wave function, there are recent experiments in atomic
physics where the classical approach provides valuable in