### Abstract

Certain Hamiltonians, based on two coupled quantum mechanical spins, exhibit degenerate eigenvalues despite having no obvious non-Abelian symmetries. Operators acting to permute the degenerate states do not have a simple form when expressed as polynomials of the generators of rotations for the respective spins. As observed in [3], one such Hamiltonian helps explain resonances in the spin relaxation rate of optically pumped Rb_{2}, as a function of applied magnetic field. We give an explanation of why the degeneracies exist, based on properties of the commutator and anti-commutator of the Hamiltonian and its image under magnetic field reversal.

Original language | English (US) |
---|---|

Pages (from-to) | 593-602 |

Number of pages | 10 |

Journal | Advances in Theoretical and Mathematical Physics |

Volume | 9 |

Issue number | 4 |

DOIs | |

State | Published - Aug 2005 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Physics and Astronomy(all)

## Fingerprint Dive into the research topics of 'Degenerate eigenvalues for Hamiltonians with no obvious symmetries'. Together they form a unique fingerprint.

## Cite this

Gubser, S. S., & Bradley, R. K. (2005). Degenerate eigenvalues for Hamiltonians with no obvious symmetries.

*Advances in Theoretical and Mathematical Physics*,*9*(4), 593-602. https://doi.org/10.4310/atmp.2005.v9.n4.a4