Schrödinger equation with delta potential in superspace. (English) Zbl 1221.81050
Summary: A superspace version of the Schrödinger equation with a delta potential is studied using Fourier analysis. An explicit expression for the energy of the single bound state is found as a function of the super-dimension \(M\) in case \(M\) is smaller than or equal to 1. In the case when there is one commuting and \(2n\) anti-commuting variables also the wave function is given explicitly.
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 15A66 | Clifford algebras, spinors |
| 46S60 | Functional analysis on superspaces (supermanifolds) or graded spaces |
| 42B10 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
References:
| [1] | De Bie, H.; Sommen, F., Adv. Appl. Clifford Alg., 17, 357 (2007) · Zbl 1129.30034 |
| [2] | De Bie, H.; Sommen, F., Ann. Phys., 322, 2978 (2007) · Zbl 1132.81017 |
| [3] | De Bie, H.; Sommen, F., J. Phys. A: Math. Theor., 40, 7193 (2007) · Zbl 1143.30315 |
| [4] | De Bie, H.; Sommen, F., J. Phys. A: Math. Theor., 40, 10441 (2007) · Zbl 1152.30052 |
| [5] | De Bie, H.; Sommen, F., J. Math. Anal. Appl., 338, 1320 (2008) · Zbl 1143.30022 |
| [6] | Finkelstein, R.; Villasante, M., Phys. Rev. D, 33, 6, 1666 (1986) |
| [7] | Delbourgo, R.; Jones, L. M.; White, M., Phys. Rev. D, 40, 8, 2716 (1989) |
| [8] | R. Zhang, Orthosymplectic Lie superalgebras in superspace analogues of quantum Kepler problems, Commun. Math. Phys., doi: 10.1007/s00220-008-0450-4; R. Zhang, Orthosymplectic Lie superalgebras in superspace analogues of quantum Kepler problems, Commun. Math. Phys., doi: 10.1007/s00220-008-0450-4 · Zbl 1154.81012 |
| [9] | H. De Bie, Fourier transform and related integral transforms in superspace, J. Math. Anal. Appl., doi: 10.1016/j.jmaa.2008.03.047; H. De Bie, Fourier transform and related integral transforms in superspace, J. Math. Anal. Appl., doi: 10.1016/j.jmaa.2008.03.047 · Zbl 1149.30037 |
| [10] | Berezin, F. A., Introduction to Algebra and Analysis with Anticommuting Variables (1983), Moskov. Gos. Univ.: Moskov. Gos. Univ. Moscow · Zbl 0527.15020 |
| [11] | Gelfand, I. M.; Shilov, G. E., Generalized Functions, vol. 1 (1964), Academic Press: Academic Press New York and London · Zbl 0115.33101 |
| [12] | H. De Bie, The purely fermionic Schrödinger equation, submitted for publication; H. De Bie, The purely fermionic Schrödinger equation, submitted for publication |
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.
