Is Work Done During Adiabatic Compression of a Quantum State?

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Discussion Overview

The discussion revolves around the concept of work done during adiabatic compression of a quantum state, specifically in the context of changes in the Hamiltonian and the implications for systems in superposition. It touches on both classical and quantum mechanics perspectives.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether work is done by an external agency during an adiabatic change in the Hamiltonian of a quantum state.
  • Another participant asserts that the change in energy of the system represents the work done on the system, applicable in both classical and quantum mechanics.
  • A participant expresses confusion regarding the definition of energy when the state is a superposition of energy levels, suggesting that this complicates the understanding of work done.
  • A specific scenario is proposed involving a particle in an infinite well, where the walls are compressed slowly while the state is in a superposition of the first and second excited levels. The participant questions why the work done should be equated to the change in expectation value of the energy.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the definition of work done in the context of quantum states in superposition, and multiple competing views remain regarding the implications of adiabatic changes and energy definitions.

Contextual Notes

Participants highlight limitations in defining energy for superposed states and the assumptions involved in relating work to changes in expectation values, which remain unresolved.

Prathyush
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Is work done by the external agency when an adiabatic change in the Hamiltonian is performed on some State ψ?
 
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Yes. We don't even need to restrict ourselves to adiabatic changes here. The change in energy of the system is the work done on the system, in classical or in quantum mechanics, essentially by definition.
 
Yes What I am confused about is if the state is superposition of energy levels, we have no adequate definition of Energy of the system.
 
I have thought of a specific situation to illustrate my problem.
Consider the case of a Particle in a infinite well, If the walls are compressed slowly and state is in a superposition of first and second excited levels, What is the work done on the walls?
One can say that the work done is the change in expectation value of the energy, But why should it be so?
 
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