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American Journal of Physics

Transport approach to one-dimensional quantum scattering

Yoel Tikochinsky

Published Nov 1, 1977• 1 citation
Publisher

Abstract

Starting from ’’first principles,’’ transport and invariant imbedding equations are derived for one-dimensional quantum scattering. The connection between the two kinds of equations is established by means of a simple transformation.
DOI
10.1119/1.10730

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1. INTRODUCTION In this chapter we shall apply the method of invariant imbedding to two types of problems that occur often in quantum mechanical studies. The first general class is frequently referred to as the “phase shift” problem, while the second is a particular form of the eigenvalue problem. In this latter case the method of the previous chapter is, within certain technical limits, applicable. However, the way in which we shall now make use of the imbedding scheme gives rise to a completely different characterization of the eigenvalues than the one we have been discussing. It seems particularly desirable to include a presentation of this method because the results illustrate so strikingly the way in which different kinds of imbeddings can yield completely different formulas. Although the phase shift problem is of less interest in itself, since our results can be derived in a rather more elementary way, we include it since once again, it demonstrates the versality of the method (see [1,2]).