Stationary Motion of a Quantum Particle in the Field of a One-Dimensional Arbitrary Potential

摘要

A new approach to the problem of description of the stationary motion of a quantumparticle in the field of a one-dimensional arbitrary potential is developed. It is shown that the wavefunction of infinite motion, with the accuracy to two arbitrary constants, can be expressed by means ofan arbitrary single solution for some set of linear differential equations of the first order. It is shownthat one general property of the Schrodinger equation solutions lies in the basis of many knownmethods of the problem consideration, such as the method of integral equations, transfer-matrixmethod, imbedding method, and method of combination of scattering parameters. Within theframework of the proposed approach, the connection between the above-mentioned methods becomesmore transparent.