literature
Literature
Authors
Jobs
Seminars
Conferences
DataBETA

Quasiexactly solvable quartic potential

1998
3 pages
Published in:
  • J.Phys.A 31 (1998) L273-L277
e-Print:
DOI:
View in:
pdf
reference search114 citations

Citations per year

1998200520122019202402468101214
Abstract:
A new two-parameter family of quasi-exactly solvable quartic polynomial potentials V(x)=−x4+2iax3+(a2−2b)x2+2i(ab−J)xV(x)=-x^4+2iax^3+(a^2-2b)x^2+2i(ab-J)x 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, PT{\cal PT}-symmetric Hamiltonians whose spectra are real, discrete, and bounded below [physics/9712001]. Replacing Hermiticity by the weaker condition of PT{\cal PT} 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 JJ eigenvalues. These eigenvalues are the roots of a JJth-degree polynomial.
Note:
  • 3 Pages, RevTex, 1 Figure, encapsulated postscript Subj-class: Mathematical Physics: Exactly Solvable and Integrable Systems Journal-ref: Journal of Physics A 31, L273-L277 (1998)