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| Paper IPM / P / 7604 |
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Introducing the associated Laguerre functions in terms of two non-negative integers, we obtain simultaneously and separately realization of the laddering equations with respect to each of the integers by means of two pairs of ladder operators. Besides, two different types of shape-invariance symmetries are realized. This approach leads to a derivation of shape-invariance equations of third type which are realized by two simultaneous raising and lowering operators of two parameters.
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