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New method for computation of discrete spectrum of radical Schrödinger operator

Ivan ÚlehlaMiloslav Havlíček — 1980

Aplikace matematiky

A new method for computation of eigenvalues of the radial Schrödinger operator - d 2 / d x 2 + v ( x ) , x 0 is presented. The potential v ( x ) is assumed to behave as x - 2 + ϵ if x 0 + and as x - 2 - ϵ if x + , ϵ 0 . The Schrödinger equation is transformed to a non-linear differential equation of the first order for a function z ( x , ) . It is shown that the eigenvalues are the discontinuity points of the function z ( , ) . Moreover, it is shown how to obtain an arbitrarily accurate approximation of eigenvalues. The method seems to be much more economical in comparison...

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