One-dimensional hydrogen atom with minimal length uncertainty and maximal momentum
Department of Physics, Science and Research Branch, Islamic Azad University - Tehran, Iran
Received: 6 December 2012
Accepted: 21 January 2013
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 agree with the semiclassical results.
PACS: 04.60.-m – Quantum gravity / 03.65.Ge – Solutions of wave equations: bound states / 03.65.Sq – Semiclassical theories and applications
© EPLA, 2013