Levinson's theorem for the Schrödinger equation in one dimension

Details Levinson's theorem for the Schrödinger equation in one dimension Levinson's theorem for the Schrödinger equation in one dimension

1999-03-04

arxiv.org/abs/quant-ph/9903016v1

Int.J.Theor.Phys. 39 (2000) 469-481

Physics

Quantum Physics

Revtex 11 pages and submitted to Phys. Rev. A

Scientific paper

10.1007/s100530070079

Levinson's theorem for the one-dimensional Schr\"{o}dinger equation with a symmetric potential, which decays at infinity faster than $x^{-2}$, is established by the Sturm-Liouville theorem. The critical case, where the Schr\"{o}dinger equation has a finite zero-energy solution, is also analyzed. It is demonstrated that the number of bound states with even (odd) parity $n_{+}$ ($n_{-}$) is related to the phase shift $\eta_{+}(0)[\eta_{-}(0)]$ of the scattering states with the same parity at zero momentum as $\eta_{+}(0)+\pi/2=n_{+}\pi, \eta_{-}(0)=n_{-}\pi$, for the non-critical case, $\eta_{+}(0)=n_{+}\pi, \eta_{-}(0)-\pi/2=n_{-}\pi$, for the critical case.

Affiliated with

Also associated with

No associations

Rating

Levinson's theorem for the Schrödinger equation in one dimension does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Levinson's theorem for the Schrödinger equation in one dimension, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Levinson's theorem for the Schrödinger equation in one dimension will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-231631