Analytical expressions of potentials and wave functions for atoms and ions

T. Mukoyama, Gábor Hock

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A method to calculate the self-consistent field (SCF) potential and wave functions for atoms and ions in analytical forms is described. The numerical SCF potential for atoms and ions is fitted to an analytical function by the use of the nonlinear least-squares method. The SCF wave functions are obtained numerically by solving the Schrödinger equation with the analytical SCF potential. The analytical wave functions are calculated with the nonlinear least-squares fitting technique. The obtained results are tested by comparing energy eigenvalues and radiative transition probabilities with those from numerical calculations.

Original languageEnglish
Pages (from-to)155-157
Number of pages3
JournalNuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and Atoms
Volume86
Issue number1-2
DOIs
Publication statusPublished - Mar 3 1994

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Wave functions
self consistent fields
wave functions
Ions
Atoms
atoms
ions
least squares method
transition probabilities
eigenvalues
energy

ASJC Scopus subject areas

  • Surfaces, Coatings and Films
  • Instrumentation
  • Surfaces and Interfaces

Cite this

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AU - Hock, Gábor

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N2 - A method to calculate the self-consistent field (SCF) potential and wave functions for atoms and ions in analytical forms is described. The numerical SCF potential for atoms and ions is fitted to an analytical function by the use of the nonlinear least-squares method. The SCF wave functions are obtained numerically by solving the Schrödinger equation with the analytical SCF potential. The analytical wave functions are calculated with the nonlinear least-squares fitting technique. The obtained results are tested by comparing energy eigenvalues and radiative transition probabilities with those from numerical calculations.

AB - A method to calculate the self-consistent field (SCF) potential and wave functions for atoms and ions in analytical forms is described. The numerical SCF potential for atoms and ions is fitted to an analytical function by the use of the nonlinear least-squares method. The SCF wave functions are obtained numerically by solving the Schrödinger equation with the analytical SCF potential. The analytical wave functions are calculated with the nonlinear least-squares fitting technique. The obtained results are tested by comparing energy eigenvalues and radiative transition probabilities with those from numerical calculations.

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