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.
Statement of theorem
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: continuous in except for a finite number of finite discontinuities
References
External links
M. Wellner, "Levinson's Theorem (an Elementary Derivation," Atomic Energy Research Establishment, Harwell, England. March 1964.