Discrete Degenerate Representations of Noncompact Rotation Groups. I

We study in detail the bound state spectrum of the generalized Morse potential (GMP), which was proposed by Deng and Fan as a potential function for diatomic molecules. By connecting the corresponding Schrödinger equation with the Laplace equation on the hyperboloid and the Schrödinger equation for the Pöschl-Teller potential, we explain the exact solvability of the problem by an so(2, 2) symmetry algebra, and obtain an explicit realization of the latter as su(1, 1) ⊕ su(1, 1). We prove that some of the so(2, 2) generators connect among themselves wave functions belonging to different GMP's (called satellite potentials). The conserved quantity is some combination of the potential parameters instead of the level energy, as for potential algebras. Hence, so(2, 2) belongs to a new class of symmetry algebras. We also stress the usefulness of our algebraic results for simplifying the calculation of Frank-Condon factors for electromagnetic transitions between rovibrational levels based on different electronic states.

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“…It is well known from the general theory of so(p, q) irreps [14], that in a given irrep depending on…”

Section: The Generalized Morse Potentialmentioning

confidence: 99%

“…characterizes the irrep of the algebra so(2, 2), belonging to the discrete series of its most degenerate unitary irreps [14].…”

Section: The Generalized Morse Potentialmentioning

confidence: 99%

Generalized Morse potential: Symmetry and satellite potentials

Mesa

Quesne

Smirnov

1998

J. Phys. A: Math. Gen.

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“…. , r, act upon basis elements (14) by the formulas of Section 3 as operators of the corresponding irreducible representations of the subalgebra so q (r). It is clear that these operators act only upon entries k, j, .…”

Section: Representations Of the Degenerate Principal Seriesmentioning

confidence: 99%

“…. , r + s, act upon basis elements (14) by formulas of Section 3 as operators of corresponding irreducible representations of the subalgebra so q (s). The operator T λ (I r+1,r ) acts upon vectors (14) by the formula…”

Section: Representations Of the Degenerate Principal Seriesmentioning

confidence: 99%

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Degenerate Series Representations of the q-Deformed Algebra so'_q(r,s)

Groza¹

2007

SIGMA

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Abstract. The q-deformed algebra so q (r, s) is a real form of the q-deformed algebra U q (so(n, C)), n = r + s, which differs from the quantum algebra U q (so(n, C)) of Drinfeld and Jimbo. We study representations of the most degenerate series of the algebra so q (r, s). The formulas of action of operators of these representations upon the basis corresponding to restriction of representations onto the subalgebra so q (r) × so q (s) are given. Most of these representations are irreducible. Reducible representations appear under some conditions for the parameters determining the representations. All irreducible constituents which appear in reducible representations of the degenerate series are found. All * -representations of so q (r, s) are separated in the set of irreducible representations obtained in the paper.

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