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Il Nuovo Cimento B

Application of generalized Hellmann-Feynman theorem in deriving internal energy of some Hamiltonians in quantum optics

Hong-Yi Fan, Min Wang, Peng Yan

Published Jun 1, 2006• 0 citations
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Abstract

In this paper, after introducing the generalized Hellmann-Feynman (or Feynman-Hellmann) theorem (GHFT) for mixed-state ensemble average, we apply GHFT to deriving the internal energy of some Hamiltonian systems in quantum optics. The ensemble average energy contributed from each separated term involved in the Hamiltonian is also considered. We thus develop an alternate approach for deriving the internal energy.

DOI
10.1393/ncb/i2006-10080-3

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In this paper, after introducing the generalized Hellmann-Feynman (or Feynman-Hellmann) theorem (GHFT) for mixed-state ensemble average, we apply GHFT to deriving the internal energy of some Hamiltonian systems in quantum optics. The ensemble average energy contributed from each separated term involved in the Hamiltonian is also considered. We thus develop an alternate approach for deriving the internal energy.
The Hellmann-Feynman theorem in a pure ensemble is extended to a quasidegenerate mixed ensemble (canonical) as an ensemble average value. The theorem is also extended to a grand canonical ensemble wherein average particle number is conserved. Connections with the thermodynamic observables are made. An approximate relation between $\ensuremath{\partial}{[\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}]}_{C}∕\ensuremath{\partial}\ensuremath{\lambda}$ and $\ensuremath{\partial}{[\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}]}_{G}∕\ensuremath{\partial}\ensuremath{\lambda}$ is established at the leading order of the saddle-point approximation.