Is Work Done During Adiabatic Compression of a Quantum State?

In summary, the conversation discusses work done by an external agency during an adiabatic change in the Hamiltonian on a state ψ. It is agreed that the change in energy of the system is the work done, regardless of whether it is classical or quantum mechanics. However, there is confusion about defining the energy of a superposition state. A specific example is given of a particle in an infinite well with compressed walls and a superposition of excited levels. It is suggested that the work done is the change in expectation value of energy, but this is questioned.
  • #1
Prathyush
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16
Is work done by the external agency when an adiabatic change in the Hamiltonian is performed on some State ψ?
 
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  • #2
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.
 
  • #3
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.
 
  • #4
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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1. What is an adiabatic change?

An adiabatic change refers to a thermodynamic process in which there is no transfer of heat between the system and its surroundings. This means that the change in internal energy of the system is solely due to work done on or by the system.

2. How is work related to an adiabatic change?

In an adiabatic change, work is the only means by which the internal energy of the system can be changed. This can be either work done on the system, resulting in an increase in internal energy, or work done by the system, resulting in a decrease in internal energy.

3. What is the formula for calculating work in an adiabatic process?

The formula for calculating work in an adiabatic process is W = -PΔV, where W is work, P is pressure, and ΔV is the change in volume of the system. This formula is based on the first law of thermodynamics, which states that the change in internal energy of a closed system is equal to the sum of heat and work.

4. Can an adiabatic change result in a change in temperature?

Yes, an adiabatic change can result in a change in temperature. This is because the change in internal energy of the system is related to the change in temperature through the specific heat capacity of the substance. Therefore, work done on or by the system can cause a change in temperature, even in the absence of heat transfer.

5. How is an adiabatic change different from an isothermal change?

An adiabatic change is different from an isothermal change in that an adiabatic change does not allow for any heat transfer between the system and its surroundings, while an isothermal change occurs at a constant temperature and allows for heat transfer. Additionally, in an adiabatic change, the change in temperature is not constant, while in an isothermal change, the change in temperature is zero.

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