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.