1 research outputs found
Quasi-exactly solvable quartic potential
A new two-parameter family of quasi-exactly solvable quartic polynomial
potentials is introduced. Until now,
it was believed that the lowest-degree one-dimensional quasi-exactly 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 non-Hermitian, -symmetric Hamiltonians
whose spectra are real, discrete, and bounded below [physics/9712001].
Replacing Hermiticity by the weaker condition of symmetry allows
for new kinds of quasi-exactly solvable theories. The spectra of this family of
quartic potentials discussed here are also real, discrete, and bounded below,
and the quasi-exact portion of the spectra consists of the lowest
eigenvalues. These eigenvalues are the roots of a th-degree polynomial.Comment: 3 Pages, RevTex, 1 Figure, encapsulated postscrip