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

Abstract

We reduce two-body problem to the one-body problem in general case of deformed Heisenberg algebra leading to minimal length. Twobody problems with delta and Coulomb-like interactions are solved exactly. We obtain analytical expression for the energy spectrum for partial cases of deformation function. The dependence of the energy spectrum on the center-of-mass momentum is found. For special case of deformation function, which correspondes to cutoff procedure in momentum space it is shown that this dependence is more likely to observe for identical particles.

Scattering in graphene quantum dots under generalized uncertainty principle

“…83,84 We first determine the scattering coefficients by using Eqs. 14, (16), (18) and considering the continuity of the wave functions at the boundary of circular barrier 77,78…”

“…The deformed momentum operators will almost inevitably cause Hamiltonians of all quantum mechanical systems to be corrected. Since Kempf and his colleagues established the theoretical framework of quantum mechanics based on generalized uncertainty, the studies of Schrödinger equation, [13][14][15][16][17][18][19][20][21][22][23][24][25][26] the Dirac equation, [27][28][29][30][31][32][33][34][35][36][37][38] K-G equation [39][40][41] and DKP equation [42][43][44][45][46][47][48][49][50] get great interest, and some phenomena in black hole remnants, 51,52 the trans-Planckian problem of inflation, 53,54 and the cosmological constant problem 55,56 can be explained by generalized uncertainty relations. On the quantum level, except for the bound state, some related works on scattering state have been reported.…”

Regularization of δ′ 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 the 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 Dirac delta function and Coulomb-like interactions [28].…”

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].…”