A new method for the solution of the Schrödinger equation

• Autor(a) principal: Canosa, José
• Data de Publicação: 1969
• Outros Autores: Oliveira, Roberto gomes de, Instituto de Engenharia Nuclear, IBM Scientific Center
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional do IEN
• Texto Completo: http://carpedien.ien.gov.br:8080/handle/ien/2710
• topic: Schrodinger equation; Eigenfunctions; Eigenvalues; Mathematical solutions

We approximate the potential in the one-dimensional Schrödinger equation by a step function with a finite number of steps. In each step, the resulting differential equation has constant coefficients and is integrated exactly in terms of circular or hyperbolic functions. The solutions are then matched at the interface of each layer to construct the eigenfunctions in the whole domain. Unique features of the numerical method are: (a) All the eigenfunctions and eigenvalues are obtained with the same absolute accuracy for the same number of steps in the potential;(b) any desired number of eigenvalues and eigenfunctions are obtained in one single pass without any need to supply initial guesses for the eigenvalues; (c) for any fixed number of steps in the potential, we obtain in principle the whole infinite spectrum of eigenvalues and eigenfunctions.