What Does h.c. Signify in Quantum Mechanics Formulas?

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Discussion Overview

The discussion centers around the interpretation of the term "h.c." in the context of an interaction Hamiltonian in quantum mechanics. Participants explore the implications of this term within the framework of quantum mechanics, particularly in relation to the operators and parameters involved in the formula.

Discussion Character

  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant identifies "h.c." as standing for Hermitean conjugate.
  • Another participant seeks clarification on how to explicitly write the second term of the Hamiltonian, questioning whether certain operators should change while others remain constant.
  • A different participant inquires about the meaning of the parameter g, suggesting it might refer to the gyromagnetic ratio.

Areas of Agreement / Disagreement

There is no consensus on the interpretation of the term "h.c." beyond the initial identification as Hermitean conjugate, and participants express uncertainty regarding the explicit formulation of the second term and the meaning of g.

Contextual Notes

Participants have not fully resolved the implications of the Hermitean conjugate in this context, nor have they clarified the roles of the operators and parameters involved in the Hamiltonian.

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A textbook gives the following interaction Hamiltonian describing the interaction of an atom (having transition dipole moment [itex]\mu[/itex]) with a photon whose polarization can be [itex]\epsilon_{1}[/itex] or [itex]\epsilon_{2}[/itex]):

H = g [itex]\Sigma[/itex][itex]^{2}_{s=1}[/itex][itex]\mu[/itex][itex]\bullet[/itex][itex]\epsilon[/itex]s[itex]\sigma^{-}[/itex]a[itex]^{+}_{s}[/itex] + h.c.

where [itex]\sigma^{-}[/itex] is Pauli spin-flip operator and a[itex]^{+}_{s}[/itex] is the creation/annihilation operator.

What does "h.c." stand for in this formula?
 
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Hermitean conjugate.
 
Thanks for the quick reply. But I still cannot quite see how to write the second term explicitly. Am I correct in assuming that μ and ϵ1, ϵ2 should not change, σ− will become σ+, and creation operator will change to annihilation operator?
 
Also, what does g stand for - gyromagnetic ratio?
 

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