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Exact wave functions for few‐particle systems: The choice of expansion for coulomb potentials
Author(s) -
McIsaac K.,
Maslen E. N.
Publication year - 1987
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560310307
Subject(s) - wave function , coulomb , bounded function , function (biology) , algebraic number , degrees of freedom (physics and chemistry) , schrödinger equation , coulomb wave function , boundary (topology) , physics , mathematics , classical mechanics , mathematical analysis , quantum mechanics , electron , evolutionary biology , biology
For exact few‐particle wave functions the choice of expansion has a strong influence on the ease with which the coefficients may be determined. Some expansions, such as those involving hyperspherical coordinates, require complicated expressions for Coulomb interaction potentials. The choice of expansion provides a possible means for minimizing algebraic problems in determining the exact wave function. The complexity due to the nonseparable terms in the potential occurs at different stages of the solution of the Schrödinger equation when the expansion is transformed. When solving recurrence relations to determine the wave function, it is necessary to understand the relationship between degrees of freedom in the solution and the boundary conditions. The degrees of freedom in the solution must be chosen to ensure that the wave function is continuous and normalizable and that the derivatives are bounded everywhere.