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The q-Coulomb problem in configuration space

We formulate the q‐Coulomb problem in configuration space with the aid of ladder operators for the radial wave function. The highest angular momentum state corresponding to the principal quantum number n is found to be the monomial rn−1 multiplied by a q‐exponential. The states of lower angular momentum are q‐associated Laguerre polynomials multiplied by the same q‐exponential. The state functions all lie in the complex plane and may be interpreted in the standard way. The energy levels are again given by a Balmer formula with n replaced by the basic n.

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