Premium
Quantum mechanical engineering of short range potentials
Author(s) -
Green A. E. S.,
Schwartz J. M.,
Suh S. T.
Publication year - 2009
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.560280839
Subject(s) - morse potential , eigenvalues and eigenvectors , range (aeronautics) , harmonic oscillator , schrödinger equation , quantum , azimuthal quantum number , physics , quantum number , electric potential , potential energy , angular momentum , quantum mechanics , total angular momentum quantum number , angular momentum coupling , voltage , materials science , composite material
The number, ordering, and bindings of the energy levels for various nodal and angular momentum quantum numbers are major indicators of the characteristics of a quantum mechanical potential. In the present study we develop explicit formulas which may be used to characterize the energy levels of a particle in a short range central potential. Such potentials arise in models of nuclear shell structure, of negative atomic ions, and of quark‐antiquark bound states. One set of formulas is inferred by adapting the Morse potential eigenvalue formula. A second set is obtained by modifying the approximations of Sukhatme, Imbo, and Pagnamenta (SIP), which display particular accuracy for power law potentials such as the coulomb potential and the harmonic oscillator potential. To improve their accuracy and utility for short range potentials we here utilize a further expansion and introduction of parameters which may be obtained approximately from derivatives of the potential. We arrive at explicit formulas which by minor adjustment conform to the critical potential magnitude parameter and to the eigenvalues for a particle in a short range potential obtained by numerical solutions of Schrodinger's equation. We use the exponential potential to illustrate the method and the results.