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

Abstract

Abstract. We present exact energy eigenvalues and eigenfunctions of the onedimensional 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.

Exact Solutions of the (2+1)-Dimensional Dirac Oscillator under a Magnetic Field in the Presence of a Minimal Length in the Non-commutative Phase Space

“…In this context, many papers were published where a different quantum system in space with the Heisenberg algebra was studied. They are the Abelian Higgs model [19], the thermostatics with minimal length [20], the one-dimensional hydrogen atom [21], the casimir effect in minimal length theories [22], the effect of minimal lengths on electron magnetism [23], the DO in one and three dimensions [24][25][26][27][28], the noncommutative (NC) (2+1)-dimensional DO and quantum phase transition [10], the solutions of a two-dimensional Dirac equation in the presence of an external magnetic field [29], the NC phase space Schrödinger equation [30], and the Schrödinger equation with harmonic potential in the presence of a magnetic field [31].…”

The exact solutions of a (2 + 1)-dimensional Dirac oscillator under a magnetic field in the presence of a minimal length

“…In this context, many papers were published where a different quantum system in space with Heisenberg algebra was studied. They are: the Abelian Higgs model [15], the thermostatics with minimal length [16], the one-dimensional Hydrogen atom [17], the casimir effect in minimal length theories [18], the effect of minimal lengths on electron magnetism [19], the Dirac oscillator in one and three dimensions [20][21][22][23][24], the solutions of a two-dimensional Dirac equation in presence of an external magnetic field [25], the noncommutative phase space Schrödinger equation [26], Schrödinger equation with Harmonic potential in the presence of a Magnetic Field [27].…”

Two-Dimensional Klein–Gordon Oscillator in the Presence of a Minimal Length

“…In the minimal length formalism, the Heisenberg algebra is given by [12][13][14][15][16][17][18][19][20][21][22][23][24]…”

“…In this context, many papers were published where a different quantum system in space with Heisenberg algebra was studied. They are: the Abelian Higgs model [15], the thermostatics with minimal length [16], the one-dimensional Hydrogen atom [17], the casimir effect in minimal length theories [18], the effect of minimal lengths on electron magnetism [19], the Dirac oscillator in one and three dimensions [20,21], the solutions of a two-dimensional Dirac equation in presence of an external magnetic field [22], the non-commutative phase space Schrodinger equation [23], Schrodinger equation with Harmonic potential in the presence of a Magnetic Field [24].…”