Supersymmetry in quantum mechanics
作者:
Richard W. Haymaker,
A. R. P. Rau,
期刊:
American Journal of Physics
(AIP Available online 1986)
卷期:
Volume 54,
issue 10
页码: 928-936
ISSN:0002-9505
年代: 1986
DOI:10.1119/1.14794
出版商: American Association of Physics Teachers
关键词: SUPERSYMMETRY;QUANTUM MECHANICS;HAMILTONIANS;MORSE POTENTIAL;MAGNETIC FIELDS;HELIUM;HYDROGEN;ATOMS;QUANTUM NUMBERS;COULOMB ENERGY;HARMONIC OSCILLATORS
数据来源: AIP
摘要:
We give some illustrations and interpretations of supersymmetry in quantum mechanics in simple models. We show that the value of 2 for thegfactor of the electron expresses the presence of supersymmetry in the Hamiltonian for an electron in a uniform magnetic field. The problem is considered both in the Schrödinger and Dirac formulations. We also show that the radial Coulomb problem with orbital angular momentuml, nuclear chargeZ, and principal quantum numbern, is supersymmetrically linked to the similar problem with chargeZ(1−1/n) and quantum numbern−1. Thereby the dependence of Coulomb energies only on the combinationZ/nis seen as a manifestation of the supersymmetry in the radial Coulomb problem. Other examples of supersymmetry we consider are the Morse potential, the three‐dimensional isotropic oscillator, the states of the helium atom and those of the hydrogen atom in an extremely strong magnetic field.
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