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

Abstract

We present exact energy eigenvalues and eigenfunctions of the one-dimensional hydrogen atom in the framework of the Generalized (Gravitational) Uncertainty Principle (GUP). This form of GUP is consistent with various theories of quantum gravity such as string theory, loop quantum gravity, black-hole physics, and doubly special relativity and implies a minimal length uncertainty and a maximal momentum. We show that the quantized energy spectrum exactly agrees with the semiclassical results.

10 pages, 1 figure

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• Kratzer's molecular potential in quantum mechanics with a generalized uncertainty principle
• Exact Ultra Cold Neutrons' Energy Spectrum in Gravitational Quantum Mechanics
• Generalized uncertainty principle and the conformally coupled scalar field quantum cosmology
• New higher-order generalized uncertainty principle: Applications
• Exact solutions of the (2+1) -dimensional Dirac oscillator under a magnetic field in the presence of a minimal length in the noncommutative phase-space
• The minimal length and the Shannon entropic uncertainty relation
• One-dimensional Coulomb-like problem in general case of deformed space with minimal length
• The solitary solutions of nonlinear Klein-Gordon field with minimal length
• Position and momentum uncertainties of a particle in a V-shaped potential under the minimal length uncertainty relation
• Two-dimensional Klein-Gordon Oscillator in the presence of a minimal length
• Hartmann potential with a minimal length and generalized recurrence relations for matrix elements
• Minimal length implications on the Hartree-Fock theory