Collect. Czech. Chem. Commun. 2008, 73, 1372-1390

Quasi-Exactly Solvable Models in Quantum Chemistry

Jacek Karwowski* and Kamil Szewc

Instytut Fizyki, Uniwersytet Mikołaja Kopernika, Grudziądzka 5, 87-100 Toruń, Poland


A separable model of N interacting particles, in which disjoint pairs of particles interact by arbitrary two-particle potentials while the remaining interactions obey the Hooke law, is discussed from a perspective of its applications in quantum chemistry. In particular, properties of three- and four-particle Hookean systems modeling He-like atoms, H2+ and H2 molecules and many exotic systems are analyzed. The energy spectra and the structure of the wavefunctions of quasi-exactly solvable Schrödinger equations which result from this analysis are investigated in some detail.

Keywords: Schrödinger equation; Quasi-exactly solvable models; Separability; Harmonium; Hookean molecules; Hamiltonian.

References: 22 live references.