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Group analysis of Schroedinger equation with generalised Kratzer type potential

Karmadeva Maharana
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Abstract

Using the method of $su(1,1)$ spectrum generating algebra, we analyze one dimensional Schroedinger equation with potential in the form ${C\over{x^2} + {D\over{x}}$ to obtain a class of potentials giving similar eigenvalues. By a group analysis of the differential equation it is found that the symmetry gets enhanced for particular values of $C$ and $D$. The generators of the Lie algebra do not close. The extension of the vector field gives rise to an interesting algebra.

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Karmadeva Maharana. 2004-01-13. Group analysis of Schroedinger equation with generalised Kratzer type potential. https://arxiv.org/abs/math-ph/0401026

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