TY - JOUR

T1 - Energy-reflection symmetry of Lie-algebraic problems

T2 - Where the quasiclassical and weak-coupling expansions meet

AU - Shifman, M.

AU - Turbiner, A.

PY - 1999/3

Y1 - 1999/3

N2 - 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

AB - 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

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U2 - 10.1103/PhysRevA.59.1791

DO - 10.1103/PhysRevA.59.1791

M3 - Article

AN - SCOPUS:0033092542

SN - 1050-2947

VL - 59

SP - 1791

EP - 1798

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 3

M1 - 1791

ER -