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We present exact energy eigenvalues and eigenfunctions of the one-dimensionalhydrogen atom in the framework of the Generalized (Gravitational) UncertaintyPrinciple (GUP). This form of GUP is consistent with various theories ofquantum gravity such as string theory, loop quantum gravity, black-holephysics, and doubly special relativity and implies a minimal length uncertaintyand a maximal momentum. We show that the quantized energy spectrum exactlyagrees with the semiclassical results.

One-dimensional hydrogen atom with minimal length uncertainty and maximal momentum