CHARGED SPIN-1/2 PARTICLE IN AN ARBITRARY MAGNETIC FIELD IN TWO SPATIAL DIMENSIONS: A SUPERSYMMETRIC QUANTUM MECHANICAL SYSTEM
| Autor: | T. E. Clark, Sherwin T. Love, S.R. Nowling |
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| Rok vydání: | 2000 |
| Předmět: |
Physics
Nuclear and High Energy Physics Particle physics Degenerate energy levels FOS: Physical sciences General Physics and Astronomy Zero-point energy Astronomy and Astrophysics High Energy Physics - Phenomenology Matrix (mathematics) symbols.namesake High Energy Physics - Phenomenology (hep-ph) Quantum mechanics symbols Ground state Wave function Hamiltonian (quantum mechanics) Eigenvalues and eigenvectors Spin-½ |
| Zdroj: | Modern Physics Letters A. 15:2105-2111 |
| ISSN: | 1793-6632 0217-7323 |
| DOI: | 10.1142/s0217732300002668 |
| Popis: | It is shown that the 2 X 2 matrix Hamiltonian describing the dynamics of a charged spin 1/2 particle with g-factor 2 moving in an arbitrary, spatially dependent, magnetic field in two spatial dimensions can be written as the anticommuator of a nilpotent operator and its hermitian conjugate. Consequently, the Hamiltonians for the two different spin projections form partners of a supersymmetric quantum mechanical system. The resulting supersymmetry algebra can then be exploited to explicitly construct the exact zero energy ground state wavefunction for the system. Modulo this ground state, the remainder of the eigenstates and eigenvalues of the two partner Hamiltonians form positive energy degenerate pairs. We also construct the spatially asymptotic form of the magnetic field which produces a finite magnetic flux and associated zero energy normalizable ground state wavefunction. Comment: 10 pages, LaTeX |
| Databáze: | OpenAIRE |
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