LETTER TO THE EDITOR: Quasiexactly solvable quartic potential
Abstract
A new twoparameter family of quasiexactly solvable quartic polynomial potentials 03054470/31/14/001/img5 is introduced. Heretofore, it was believed that the lowestdegree onedimensional quasiexactly solvable polynomial potential is sextic. This belief is based on the assumption that the Hamiltonian must be Hermitian. However, it has recently been discovered that there are huge classes of nonHermitian, 03054470/31/14/001/img6symmetric Hamiltonians whose spectra are real, discrete, and bounded below. Replacing hermiticity by the weaker condition of 03054470/31/14/001/img6 symmetry allows for new kinds of quasiexactly solvable theories. The spectra of this family of quartic potentials discussed here are also real, discrete and bounded below and the quasiexact portion of the spectra consists of the lowest J eigenvalues. These eigenvalues are the roots of a Jthdegree polynomial.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 April 1998
 DOI:
 10.1088/03054470/31/14/001
 arXiv:
 arXiv:physics/9801007
 Bibcode:
 1998JPhA...31L.273B
 Keywords:

 Mathematical Physics;
 Condensed Matter;
 High Energy Physics  Theory;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Quantum Physics
 EPrint:
 3 Pages, RevTex, 1 Figure, encapsulated postscript