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Levinson's theorem

From Wikipedia, the free encyclopedia

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.[1]

Statement of theorem

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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:[2]

continuous in except for a finite number of finite discontinuities

References

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  1. ^ Levinson's Theorem
  2. ^ A. Galindo and P. Pascual, Quantum Mechanics II (Springer-Verlag, Berlin, Germany, 1990).
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