The spin-one Duffin-Kemmer-Petiau oscillator in uniform magnetic field is studied in noncommutative formalism. The corresponding energy is obtained and thereby the corresponding thermal properties are obtained for both commutative and noncommutative cases.
The first-order relativistic Duffin-Kemmer-Petiau (DKP) equation has been frequently used to study interactions of spin-one/zero particles [
On the other hand, we have motivating evidences that we have to work on the noncommutative (NC) formulation of quantum mechanics where the position or momentum operators have nonvanishing commutations. During the past years, some important problems have been investigated in the NC formalism [
Due to the physical significance of the magnetic field, Pacheco et al. studied the thermal properties of the one-dimensional Dirac oscillator problem [
One way to deal with the NC space is to construct a new kind of field theory, changing the standard product of the fields by the star product (
Assuming
Equations (
The partition function of the DKP oscillator at temperature
Entropy is related to the other quantities with the relations
We obtained the statistical quantities of the charged DKP oscillator in a uniform magnetic field in the NC space in
Energy spectra
|
|
---|---|
|
2.1820 |
|
2.2542 |
|
2.3242 |
|
2.3922 |
|
2.4583 |
|
2.5226 |
|
2.8639 |
|
2.9193 |
|
2.9737 |
|
3.0271 |
|
3.0796 |
|
3.1312 |
|
3.4122 |
|
3.4588 |
|
3.5048 |
|
3.5503 |
|
3.5951 |
|
3.6394 |
|
3.8838 |
|
3.9248 |
|
3.9654 |
|
4.0056 |
Energy spectra
|
|
---|---|
|
2.0597 |
|
2.1579 |
|
2.2519 |
|
2.3402 |
|
2.4288 |
|
2.5127 |
|
2.6591 |
|
2.7359 |
|
2.8106 |
|
3.8833 |
|
3.9543 |
|
3.0235 |
|
3.1463 |
|
3.2114 |
|
3.2753 |
|
3.3379 |
|
3.3994 |
|
3.4598 |
|
3.5676 |
|
3.6252 |
|
3.6818 |
|
3.7377 |
The comparison of the
The comparison of the partition functions for both commutative and noncommutative cases.
The comparison of the Helmholtz free energy
The NU method, named after Nikiforov and Uvarov, can solve a wide class of ordinary differential equations at most of second order. It has been already applied to other wave equations of quantum mechanics including Schrödinger, Dirac, Klein-Gordon, and Duffin-Kemmer-Petiau (DKP) equations. Here, for the sake of simplicity, we use its parametric version which solves a second-order differential equation of the form [
The partition function
The authors declare that there is no conflict of interests regarding the publication of this paper.
We wish to give our sincere gratitude to the referee for his technical comments.