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| Paper IPM / P / 6836 |
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| Abstract: | |
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Using the idea of shape invariance with respect to the main
quantum number n, we construct here new generators for the
realization of commutative relations of Lie algebra
gl(2,c). By an appropriate parametrization, new quantum
solvable Hamiltonians with dynamical symmetry group GL(2,c)
and infinite-fold degeneracy are derived. These models correspond
to the motion of a free particle on SL(2,c)/GL(1,c).
It is shown that the related quantum states satisfy shape
invariance equations with respect to n, and they also represent
the Lie algebra gl(2,c).
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