A generalized bosonic oscillator in the presence of a minimal length

Abstract

We present an exact solution of the three-dimensional Duffin–Kemmer–Petiau oscillator for spins 1 and 0 in the momentum space with the presence of minimal length uncertainty by the technique of vector spherical harmonics. The eigenfunctions are determined for both cases and the energy eigenvalues equation are obtained. The limiting case is then deduced for a small parameter of deformation.

Quantum Speed Limit for Relativistic Spin-0 and Spin-1 Bosons on Commutative and Noncommutative Planes

“…Some geometrical phases in noncommutative relativistic quantum theory are studied in [34][35][36] recently. DKP equation in noncommutative space, especially the DKP oscillator in noncommutative space, has also been investigated by some authors [37][38][39][40][41][42]. Interestingly, it is found that the noncommutativity even has some relationships with Jaynes-Cumming model in quantum optics context [43].…”

Quantum dynamics of scalar bosons in a cosmic string background

“…Using the line element (17) and the representation for the curved-space beta matrices (19), (20), (21), and (22) the condition (13) is satisfied and therefore the current is conserved for this background. Having set up the DKP equation in a cosmic string background, we are now in a position to use the machinery developed above in order to solve the DKP equation in this background with some specific forms for the external interactions.…”

“…The name distinguishes it from the system called a DKP oscillator with Lorentz tensor couplings of Ref. [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Hydrogen atom in momentum space with a minimal length

“…[4][5][6][7][8][9][10][11][12][13]. The idea of modifying the standard Heisenberg uncertainty relation in such a way that it includes a minimal length has first been proposed in the context of quantum gravity and string theory [14,15].…”