Quasi-exactly solvable cases of an N-dimensional symmetric decatic anharmonic oscillator

Feng Pan, Louisiana State University
J. R. Klauder, University of Florida
J. P. Draayer, Louisiana State University


The spectral problem of an O(N) invariant decatic anharmonic oscillator in N dimensions is considered for quasi-exactly solvable cases. The sextic anharmonic oscillator is a special case. The eigenvalue problem is found to be equivalent to that of an energy-dependent non-linear sl2 rotor. The N dependence, in the large N limit, of the ground state energies for anharmonic polynomial potentials of degree 2n is also considered. © 1999 Published by Elsevier Science B.V. All rights reserved.