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Journal of Sichuan Normal University

The Fast Calculation Method of the Average Value〈nα│ x~s│nα〉for the Hydrogen-like Atom and the Isotropic Oscillator

Long Shu-ming

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

Based on the neighbour relation of the coordinate exponential function average value 〈nα │ x~s│ nα 〉 for the isotropic oscillator and the hydrogen-like atom,the fast calculation process of this average value is shown by a brief calculation method.The Mathematica source program code is afforded,it is used in calculation for the wave function and the average value.

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Based on the neighbour relation of the coordinate exponential function average value 〈nα │ x~s│ nα 〉 for the isotropic oscillator and the hydrogen-like atom,the fast calculation process of this average value is shown by a brief calculation method.The Mathematica source program code is afforded,it is used in calculation for the wave function and the average value.
The radial functions for the discrete levels of Dirac's relativistic hydrogenic atom are expressed in terms of the generalized Laguerre polynomials which have known properties. This leads to an easy method of evaluating the normalization constants and the average values of rq{r}^{q}rq.
Being comparable in quantum systems makes it possible for spaces with varying dimensions to attribute each other using special conversions can attribute schrodinger equation with like-hydrogen atom potential in defined dimensions to a schrodinger equation with other certified dimensions with isotropic oscillator potential. Applying special transformation provides a relationship between different dimensions of two quantum systems. The result of the quantized isotropic oscillator can be generalized to like-hydrogen atom problem in different dimensions. The connection between coordinate spaces in different dimensions can follow a specific relation that by using it and applying the parametric definition in two problems, energy spectrum and like-hydrogen atom potential wave functions problem will be solved.