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Potenciais delta revisitados via transformada de Fourier (Delta potentials revisited via Fourier transform)

Antonio S. de Castro

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

The problem of bound states in delta potentials is revisited by means of Fourier transform approach. The problem in a simple delta potential sums up to solve an algebraic equation of degree one for the Fourier transform of the eigenfunction and the problem for more than one delta function also reveals itself to be a simple matter. Quite differently from direct methods, no knowledge about the jump discontinuity of the first derivative of the eigenfunction is required to determine the solution of the problem.

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The problem of bound states in delta potentials is revisited by means of Fourier transform approach. The problem in a simple delta potential sums up to solve an algebraic equation of degree one for the Fourier transform of the eigenfunction and the problem for more than one delta function also reveals itself to be a simple matter. Quite differently from direct methods, no knowledge about the jump discontinuity of the first derivative of the eigenfunction is required to determine the solution of the problem.
The problem of bound states in delta potentials is revisited by means of Fourier transform approach. The problem in a simple delta potential sums up to solve an algebraic equation of degree one for the Fourier transform of the eigenfunction and the problem for more than one delta function also reveals itself to be a simple matter. Quite differently from direct methods, no knowledge about the jump discontinuity of the first derivative of the eigenfunction is required to determine the solution of the problem.
O problema de estados ligados em potenciais delta é revisitado usando uma abordagem baseada na transformada de Fourier. O problema de um simples potencial delta resume-se à resolução de uma equação algébrica de primeiro grau para a transformada de Fourier da autofunção e o problema para mais que uma função delta também revela-se uma questão simples. Diferentemente de métodos diretos, nenhum conhecimento acerca da descontinuidade de salto da derivada primeira da autofunção é necessário para determinar a solução do problema.