### Abstract

To obtain the explicit form of evolution operator in the Tavis-Cummings model we must calculate the term e^{-itg(S+⊗a+S-⊗a†)} explicitly which is very hard. In this paper we try to make the quantum matrix A ≡ S_{+}⊗a+S_{-}⊗a^{†} diagonal to calculate e^{-itgA} and, moreover, to know a deep structure of the model. For the case of one, two and three atoms we give such a diagonalization which is the first nontrivial examples as far as we know, and reproduce the calculations of e^{-itgA} given in quant-ph/0404034. We also give a hint to an application to non-commutative differential geometry. However, a quantum diagonalization is not unique and is affected by some ambiguity arising from the non-commutativity of operators in quantum physics. Our method may open a new point of view in mathematical or quantum physics.

Original language | English |
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Pages (from-to) | 425-440 |

Number of pages | 16 |

Journal | International Journal of Geometric Methods in Modern Physics |

Volume | 2 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2005 Jun 1 |

Externally published | Yes |

### Keywords

- Evolution operator
- Non-commutativity
- Quantum diagonalization
- Tavis-Cummings model

### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

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## Cite this

*International Journal of Geometric Methods in Modern Physics*,

*2*(3), 425-440. https://doi.org/10.1142/S021988780500065X