Exact supersymmetry in the nonrelativistic hydrogen atom

Abstract

We consider a Pauli particle in a Coulomb field. The supersymmetric Hamiltonian is constructed, by explicitly giving the two supercharges $Q_1$ and $Q_2$ in the full three-dimensional space and which together with the Hamiltonian, are shown to constitute an $S(2)$ superalgebra. This offers an alternative way of grouping the energy eigenstates into irreducible representations of this symmetry group of the Hamiltonian.

15 pages

Cited by in corpus (11)

• The Quantum Mechanics SUSY Algebra: An Introductory Review
• Parametric symmetries in exactly solvable real and P T symmetric complex potentials
• Group theoretic approach to rationally extended shape invariant potentials
• Exact supersymmetry in the relativistic hydrogen atom in general dimensions -- supercharge and the generalized Johnson-Lippmann operator
• On the Hydrogen Atom via Wigner-Heisenberg Algebra
• Supersymmetry in the Majorana Cooper-Pair Box
• Shape Invariance and Its Connection to Potential Algebra
• Teaching the hidden symmetry of the Kepler problem in relativistic quantum mechanics - from Pauli to Dirac electron
• An "Accidental" Symmetry Operator for the Dirac Equation in the Coulomb Potential
• On the supersymmetry of the Dirac-Kepler problem plus a Coulomb-type scalar potential in D+1 dimensions and the generalized Lippmann-Johnson operator
• Algebraic Shape Invariant Potentials as the Generalized Deformed Oscillator