Definition of Hamiltonian Density & Deriving Energy Current

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The discussion revolves around the definition of Hamiltonian density and the derivation of energy current in quantum mechanics. Participants explore the continuity equation for energy, highlighting the need for the energy-momentum tensor to derive energy current expressions. There is a comparison between deriving electron current density and energy current density, with participants expressing frustration over the complexity of the latter. References to Weinberg's work are made, but participants seek simpler forms akin to particle current expressions. Ultimately, the conversation emphasizes the importance of understanding the underlying principles and mathematical tools to derive energy current accurately.
  • #31
daudaudaudau said:
Great. What do you think about my treatment of the external potential in my post #28 ? The one-body potential V(r) always disappears for the particle current, so does it also disappear for the energy current?
No; one gets contributions from the spatial derivatives of the interaction potential. I haven't time to look at the details of your derivation but an explicit formula is given at the end of Section 7H ''Microscopic balance equations (quantum fluids)'' of Reichl's Modern Course in Statistical Physics.
 

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