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