Massachusetts Institute of Technology

Department of Physics

Physics 8.04 Wed Oct 11 20:51:26 EDT 1995

The basic idea behind semi-classical, or Bohr-Sommerfeld quantization,
is that we may determine the allowed quantized states of a system by
performing a classical analysis of the motion and then insisting, that
in order to avoid destructive interference, there are exactly an
integral number of de Broglie wavelengths around the orbit or one
period of the classical motion. Mathematically, if **q** is the
coordinate of the particle (usually written ``**r**" in three dimensions
or ``**x**" in one) and **p** as its momentum, then

or,

Note that this is an approximate and not an exact condition because by looking at classical trajectories we are ignoring many details of the wave function.

Wed Oct 11 20:51:17 EDT 1995