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原子与分子物理学报

Explicit expressions and recurrence formulas of radial average value for N—dimensional hydrogen atom

CHENChang-yuan, SUNDong-sheng

Published Jan 1, 2002• 0 citations
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Abstract

In this paper, two recurrence formulas for radial average values of N-dimensional hydrogen atom are derived. Explicit results can be applied to discuss average value of centrifugal potential energy and other physical quantities. The relevant results of the usual hydrogen atom are contained in more general conclusion of this paper as special cases.

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CRC Press eBooks•Jan 15, 2021•0 citations
In this paper, two recurrence formulas for radial average values of N-dimensional hydrogen atom are derived. Explicit results can be applied to discuss average value of centrifugal potential energy and other physical quantities. The relevant results of the usual hydrogen atom are contained in more general conclusion of this paper as special cases.
The isotropic harmonic oscillator is one of the potential fields with strict solution.There is important significance to discuss and study it in theory and application.In this paper the recurrence formula for radial matrix elements 〈n_rl｜r~k｜n′_rl′〉 of N-dimensional isotropic harmonic oscillator is derived and on the basis of it we obtain the recurrence formula for the expectation values.We discuss the common property of the recurrence formula for radial matrix elements,however,in Refs[3] and [4] the recurrence formula for radial matrix elements are only the examples of the result in this paper.
This chapter begins with the simple solution of the Schrödinger equation for hydrogen atom for which the energy value has been derived. The Bohr radius of H atom has also been computed. After this, this chapter provides the generalised solution of the Schrödinger equation for H atom/hydrogen-like species in which F equation, R equation, and T equations have been derived in a simple and lucid way. This chapter also deals with the Laguerre differential equation, Laguerre polynomials, Rodrigues formula for the Laguerre polynomials, Laguerre associated equation and its solution, associated Laguerre polynomials, Rodrigues formula for the associated Laguerre polynomials, and solution of the radial equation. It also provides normalisation of the radial wave function and complete wave function; for the hydrogen atom, hydrogenic atomic orbital; electron density of 1 s electron; mathematical background of shape of orbitals; the most probable distance of electron from nucleus of hydrogen atom, and average distance of electron from the nucleus of hydrogen atom. The end of this chapter describes the references and adequate computational problems (solved problems and question on concepts).