Matching conditions on wave functions at discontinuities of the potential

Taksu Cheon, T Shigehara

OLLE BRANDER

Fang Jing-huai

According to mathematical principles the article rigidly deduces from Schrodinger equation the continuity conditions of wave-function and its first rank differential.They will continue if potential function continues,or if it doesn't continue but has a bound in the contiguity of the discontinuous point.However,the continuity of wave-function and its first rank differential will be uncertain if potential function is discontinuous,and boundless in the contiguity of the discontinuous point.

David Branson

Several standard arguments which attempt to show that the wave function and its derivative must be continuous across jump discontinuities of the potential are reviewed and their defects discusssed. Three arguments which it is hoped are more satisfactory are then presented.

Miloslav Znojil

We propose a new approach to the Rayleigh-Schrödinger perturbation expansions of bound states in quantum mechanics. We are inspired by the enormous flexibility of solvable interactions with several (N) discontinuities. Their standard matching solution is modified and transferred in perturbation regime. We employ the global renormalization freedom of the local wave functions and derive a compact N-dimensional matrix formula for corrections. In applications, our recipe is shown non-numerical for all polynomial perturbations of any piece-wise constant zero order potential.

Roger Colbeck, Renato Renner