Rectangular Well as Perturbation

Details Rectangular Well as Perturbation Rectangular Well as Perturbation

1997-12-18

arxiv.org/abs/quant-ph/9712041v1

J.Math.Phys. 40 (1999) 1163-1179

Physics

Quantum Physics

19 pages, 5 Postscript figures, uses psfig.sty

Scientific paper

10.1063/1.532794

We discuss a finite rectangular well as a perturbation for the infinite one with a depth $\lambda^2$ of the former as a perturbation parameter. In particular we consider a behaviour of energy levels in the well as functions of complex $\lambda$. It is found that all the levels of the same parity are defined on infinitely sheeted Riemann surfaces which topological structures are described in details. These structures differ considerably from those found in models investigated earlier. It is shown that perturbation series for all the levels converge what is in contrast with the known results of Bender and Wu. The last property is shown to hold also for the finite rectangular well with Dirac delta barier as a perturbation considered earlier by Ushveridze.

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