Determination of a Ground State Wavefunction for Helium in Momentum Space.
Abstract
The helium atom nonrelativistic Hamiltonian is considered in coordinate space. Terms representing the electrostatic interaction energy of each helium atomic electron with the nuclear electric charge are retained in the Hamiltonian. The atomic electronelectron electrostatic interaction energy is replaced with Fontana's onecenter expansion of the energy. This helium Hamiltonian with Fontana's expansion is used to express the corresponding helium Schrodinger equation in coordinate space. Application of the Fourier transformation to the helium coordinate space Schrodinger equation gives three integral terms called the kinetic energy, nuclearelectron, and electronelectron integrals. The Dirac transformation defines the coordinate space wavefunction in terms of the momentum space wavefunction and is used to evaluate the kinetic energy integral. The result is the momentum and energy operators acting on the momentum space wavefunction.
 Publication:

Ph.D. Thesis
 Pub Date:
 1978
 Bibcode:
 1978PhDT........71S
 Keywords:

 Physics: Atomic;
 Ground State;
 Helium Atoms;
 Wave Functions;
 Dirac Equation;
 Fourier Transformation;
 Hamiltonian Functions;
 Integral Equations;
 Kernel Functions;
 Kinetic Energy;
 Laplace Transformation;
 Particle Interactions;
 Schroedinger Equation;
 Atomic and Molecular Physics