Wavelets in curvilinear coordinate quantum calculations: H_{2}^{+} electronic states
Abstract
Multiscale wavelets are used to solve the quantum eigenvalue equations for the hydrogen molecular ion H2+ in the BornOppenheimer approximation. Normally restricted to Cartesian systems, "wavelets on the interval" (a normal wavelet family augmented by special edge functions) have recently been applied to such boundary value problems as the hydrogen atom in spherical polar coordinates [J. Mackey, J. L. Kinsey, and B. R. Johnson, J. Comp. Phys. 168, 356 (2001)]. These methods are extended here to ground and excited electronic states of the simplest molecule, for which the electronic Hamiltonian is separable in confocal elliptic coordinates. The set of curvilinear coordinate quantum systems for which wavelet bases have been applied is thus enlarged.
 Publication:

Journal of Chemical Physics
 Pub Date:
 August 2002
 DOI:
 10.1063/1.1494798
 Bibcode:
 2002JChPh.117.3548M
 Keywords:

 hydrogen ions;
 positive ions;
 wavelet transforms;
 eigenvalues and eigenfunctions;
 quantum theory;
 boundaryvalue problems;
 ground states;
 excited states;
 Algebra;
 BornOppenheimer Approximation;
 Boundary Value Problems;
 Eigenvalues;
 Eigenvectors;
 Electron States;
 Excitation;
 Ground State;
 Hydrogen Ions;
 Molecular Ions;
 Positive Ions;
 Quantum Theory;
 Spherical Coordinates;
 Wavelet Analysis;
 31.15.p;
 02.10.Ud;
 Atomic and Molecular Physics;
 Calculations and mathematical techniques in atomic and molecular physics;
 Linear algebra