Orbital magnetic moment of the electron in the hydrogen atom in a deformed space with minimal length

Abstract

We investigated the orbital magnetic moment of electron in the hydrogen atom in deformed space with minimal length. It turned out that corrections to the magnetic moment caused by deformation depend on one parameter in the presence of two-parametric deformation. It is interesting to note that the correction to orbital magnetic moment is similar to the correction that follows from relativistic theory but it has an opposite sign. Using the upper bound for minimal length obtained in previous papers we estimated the upper bound for relative correction to orbital magnetic moment and obtained the value ∼ 10 −12 . This is four power less than the relative error for most recent experimental values of Bohr magneton.

Deformed Heisenberg algebra with minimal length and the equivalence principle

“…One of the main results of the paper is the expression for the parameter of deformation for particles or bodies of different mass (20) which recovers the equivalence principle and thus the equivalence principle is reconciled with the generalized uncertainty principle. It is necessary to stress that expression (20) was derived also in section 3 from the condition of the independence of kinetic energy on composition. Note that (20) contains the same constant γ for different particles and parameter of deformation is inverse to the squared mass.…”

“…It is necessary to stress that expression (20) was derived also in section 3 from the condition of the independence of kinetic energy on composition. Note that (20) contains the same constant γ for different particles and parameter of deformation is inverse to the squared mass. The constant γ has dimension inverse to velocity.…”

Regularization of 1/X2 potential in general case of deformed space with minimal length

“…The study of the effect of the minimal length on systems with singular potentials or point interactions is of particular interest, since such systems are expected to have a nontrivial sensitivity to minimal length. The impact of the minimum length has been studied in the context of the following problems with singularity in potential energy: hydrogen atom [9][10][11][12][13][14][15][16], gravitational quantum well [17][18][19], a particle in delta potential and double delta potential [20,21], one-dimensional Coulomb-like problem [21][22][23], particle in the singular inverse square potential [24][25][26][27], two-body problems with delta and Coulomb-like interactions [28].…”

Two-particle system with harmonic oscillator interaction in noncommutative phase space

“…In recent years because of the development of the String Theory and Quantum Gravity (see, for example, [3,4]) the interest in the studies of noncommutativity has risen significantly. Different problems were studied in the framework of different types of noncommutativity, among them the harmonic oscillator [5][6][7][8][9][10][11][12][13], the hydrogen atom [10,[14][15][16][17][18][19][20][21][22][23][24][25][26][27][28], the Landau problem [29][30][31][32], the gravitational quantum well [33,34], classical systems with various potentials [35][36][37][38][39][40], many-particle systems [10,14,[42][43][44][45][46], and many others.…”