×

Pauli-Hamiltonian in the presence of minimal lengths. (English) Zbl 1112.81003

Summary: We construct the Pauli-Hamiltonian on a space where the position and momentum operators obey generalized commutation relations leading to the appearance of a minimal length. Using the momentum space representation we determine exactly the energy eigenvalues and eigenfunctions for a charged particle of spin half moving under the action of a constant magnetic field. The thermal properties of the system in the regime of high temperatures are also investigated, showing a magnetic behavior in terms of the minimal length.

MSC:

81P05 General and philosophical questions in quantum theory
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1063/1.530798 · Zbl 0877.17017 · doi:10.1063/1.530798
[2] DOI: 10.1103/PhysRevD.52.1108 · doi:10.1103/PhysRevD.52.1108
[3] DOI: 10.1088/0305-4470/30/6/030 · Zbl 0930.58026 · doi:10.1088/0305-4470/30/6/030
[4] DOI: 10.1063/1.531501 · Zbl 0883.46049 · doi:10.1063/1.531501
[5] DOI: 10.1142/S0217732304015919 · Zbl 1065.81608 · doi:10.1142/S0217732304015919
[6] DOI: 10.1103/PhysRevD.70.105003 · doi:10.1103/PhysRevD.70.105003
[7] DOI: 10.1016/j.physletb.2004.07.056 · doi:10.1016/j.physletb.2004.07.056
[8] DOI: 10.1088/0305-4470/33/46/311 · Zbl 1065.81506 · doi:10.1088/0305-4470/33/46/311
[9] DOI: 10.1103/PhysRevD.51.2584 · doi:10.1103/PhysRevD.51.2584
[10] DOI: 10.1103/PhysRevD.51.2584 · doi:10.1103/PhysRevD.51.2584
[11] DOI: 10.1103/PhysRevD.51.2584 · doi:10.1103/PhysRevD.51.2584
[12] DOI: 10.1142/S0217751X95000085 · doi:10.1142/S0217751X95000085
[13] DOI: 10.1016/S0370-1573(03)00059-0 · Zbl 1042.81581 · doi:10.1016/S0370-1573(03)00059-0
[14] DOI: 10.1016/S0370-1573(03)00059-0 · Zbl 1042.81581 · doi:10.1016/S0370-1573(03)00059-0
[15] DOI: 10.1016/S0370-1573(03)00059-0 · Zbl 1042.81581 · doi:10.1016/S0370-1573(03)00059-0
[16] DOI: 10.1103/PhysRevD.59.065011 · doi:10.1103/PhysRevD.59.065011
[17] Micu Andrei, J. High Energy Phys. 0101 pp 025– (2001) · doi:10.1088/1126-6708/2001/01/025
[18] DOI: 10.1103/PhysRevD.65.125027 · doi:10.1103/PhysRevD.65.125027
[19] DOI: 10.1103/PhysRevD.65.125028 · doi:10.1103/PhysRevD.65.125028
[20] DOI: 10.1103/PhysRevD.66.026003 · doi:10.1103/PhysRevD.66.026003
[21] DOI: 10.1088/0305-4470/39/9/010 · Zbl 1084.81044 · doi:10.1088/0305-4470/39/9/010
[22] DOI: 10.1088/0305-4470/32/44/308 · Zbl 0991.81047 · doi:10.1088/0305-4470/32/44/308
[23] DOI: 10.1016/j.physletb.2003.07.084 · Zbl 1031.81530 · doi:10.1016/j.physletb.2003.07.084
[24] DOI: 10.1103/PhysRevA.72.012104 · doi:10.1103/PhysRevA.72.012104
[25] DOI: 10.1088/0305-4470/39/18/025 · Zbl 1091.81017 · doi:10.1088/0305-4470/39/18/025
[26] DOI: 10.1088/0305-4470/38/8/011 · Zbl 1061.81023 · doi:10.1088/0305-4470/38/8/011
[27] DOI: 10.1088/0305-4470/38/46/009 · Zbl 1079.81065 · doi:10.1088/0305-4470/38/46/009
[28] DOI: 10.1016/j.physletb.2005.10.045 · doi:10.1016/j.physletb.2005.10.045
[29] Gradshteyn I. S., Tables of Integrals, Series and Products (1980) · Zbl 0521.33001
[30] Greiner W., Thermodynamique et Mécanique Statistique (1999)
[31] DOI: 10.1088/0305-4470/34/47/319 · Zbl 1017.81027 · doi:10.1088/0305-4470/34/47/319
[32] DOI: 10.1016/j.physletb.2005.11.004 · Zbl 1247.83113 · doi:10.1016/j.physletb.2005.11.004
[33] DOI: 10.1016/j.physletb.2005.11.004 · Zbl 1247.83113 · doi:10.1016/j.physletb.2005.11.004
[34] DOI: 10.1063/1.1504484 · Zbl 1060.81624 · doi:10.1063/1.1504484
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.