Abstract
We construct a class of one-dimensional Lie-algebraic problems based on sl(2), where the spectrum in the algebraic sector has a dynamical symmetry E↔ - E. All 2j+l eigenfunctions in the algebraic sector are paired and inside each pair are related to each other by a simple analytic continuation x→ix, except the zero mode appearing if j is integer. At j→∞ the energy of the highest level in the algebraic sector can be calculated by virtue of the quasiclassical expansion, while the energy of the ground state can be calculated as a weak-coupling expansion. Both series coincide identically
Original language | English (US) |
---|---|
Article number | 1791 |
Pages (from-to) | 1791-1798 |
Number of pages | 8 |
Journal | Physical Review A - Atomic, Molecular, and Optical Physics |
Volume | 59 |
Issue number | 3 |
DOIs | |
State | Published - Mar 1999 |