Quasiexact solution of a relativistic finite-difference analogue of the Schrodinger equation for a rectangular potential well

摘要

We consider a well-posed formulation of the spectral problem for a relativistic analogue of the one-dimensional Schrodinger equation with differential operators replaced with operators of finite purely imaginary argument shifts exp(±ihd/dx). We find effective solution methods that permit determining the spectrum and investigating the properties of wave functions in a wide parameter range for this problem in the case of potentials of the type of a rectangular well. We show that the properties of solutions of these equations depend essentially on the relation between h and the parameters of the potential and a situation in which the solution for h 1 is nevertheless fundamentally different from its Schrodinger analogue is quite possible.