Wave-Packet Scattering in a One-Dimensional Potential Step

Chandan Kumar

Francis Stephen Uralil

The purpose of this investigation is to contribute to the theory of one-dimensional scattering through a thorough study of the two-step potential. For this purpose we have studied the effect of changing a simple square well potential near its edge by adding a second step. The problem is treated using both perturbational and non-perturbational methods. The order of procedure is: (1) a general introduction, (2) multiple reflections of a wave packet by an attractive potential well, (3) discussion of the- two-step potential using perturbation theory, (4) calculation of depth of potential well for zero energy resonance, (5) conclusion.

Hiromichi Nakazato

M. Ochiai, Shunsuke Shibayama

A bstract One-dimensional scattering of a wave packet of a relativistic fermion under a temporally oscillating electric field superimposed on a potential step is discussed by using the Furry-picture perturbation theory, where the oscillating electric field is treated as a perturbation. Reflection and transmission probabilities of the wave packet, which in its single-mode limit are consistent with those in the stationary scattering off the potential step alone, are investigated up to the second order. We show that even in the absence of the so-called Klein region, a positive-frequency incoming wave can penetrate the negative- frequency region below the potential step by emitting its energy to the oscillating electric field with a finite tunneling probability.

Bernard Diu

In many quantum mechanics courses, plane waves and wave packets are introduced at the very beginning, and used to solve 'simple' one-dimensional problems with square potentials. The purpose of this article is to clarify and criticise the meaning of commonly used statements such as: 'an e ikx term represents a particle moving in the positive x direction' and/or 'e iks represents the incident beam of particles'. The necessary notions and results are first briefly reviewed. A simple problem (scattering by a one-dimensional square potential step) is then studied in detail in order to exhibit and discuss the difficulties in a concrete situation. The more general relevance of this discussion is finally indicated.

F. Bunchaft, C.M. Chaves, W. Baltensperger