Regularization of the Diracδpotential with minimal length

Influence of a minimal length on the creation of scalar particles

“…We note, also, that the quantum corrections to the black hole thermodynamics to all orders in the Planck length from a generalized uncertainty principle are calculated in [39]. This kind of studies is motivated by the possibility it offers to put the existence of a minimal length into evidence and the regularization of certain problems in physics (see for instance [33,40]). Furthermore, as is mentioned in [41], since the presence of a minimal length is common to many theories, phenomena such as the Hawking effect and the particle creation, should be critically reviewed.…”

One-dimensional Coulomb-like problem in general case of deformed space with minimal length

“…Thus, (14) together with (18) presents the definition of the square inverse distance operator in representation (3). Note, that K(±b, p ) = 0, which means that the action of the square inverse distance operator returns the wavefunction belonging to the domain of square distance operator (9).…”

“…where K(p, p ) is given by (18). By changing p for −p in (19) we can show that the Hamiltonian commutes with the parity operator, thus its eigenfunctions can be chosen as even or odd functions, i.e.…”

“…The implications of non-zero minimal length were considered in the context of the following problems with singularity in potential energy: hydrogen atom [8][9][10][11][12][13][14], gravitational quantum well [15][16][17], a particle in delta potential and double delta potential [18,19], one-dimensional Coulomb-like problem [19][20][21], particle in the singular inverse square potential [22][23][24].…”

Exact solutions for two-body problems in 1D deformed space with minimal length

“…Three-dimensional Coulomb problem with deformed Heisenberg algebra was studied within the perturbation theory in the nonrelativistic case [20][21][22][23][24] and in the case of Lorentz-covariant deformed algebra [25,26]. The problem of the D-dimensional delta potential in the first order in parameter of deformation is considered in [27]. Numerical result for hydrogen atom spectrum in a space with deformed commutation relation was obtained in [21].…”