Levinson's theorem
Levinson's theorem is an important theorem in non-relativistic quantum scattering theory. It relates the number of bound states of a potential to the difference in phase of a scattered wave at zero and infinite energies. It was published by Norman Levinson in 1949.The difference in the -wave phase shift of a scattered wave at zero energy,, and infinite energy,, for a spherically symmetric potential is related to the number of bound states by:
where or. The case is exceptional and it can only happen in -wave
scattering.
The following conditions are sufficient to guarantee the theorem:
