I Energy levels generally invariant under fixed V, changing T

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When the volume of a system is fixed and temperature increases, the occupancy of energy levels changes, but the energy levels themselves remain invariant due to constant boundary conditions in the time-independent Schrödinger equation (TISE). The energy levels are determined by the system's potential and boundary conditions, which do not vary with temperature. Temperature influences the distribution of particles among these energy levels rather than altering the levels themselves. In thermodynamics, temperature reflects the average kinetic energy of particles, affecting occupancy but not the fundamental energy states. Thus, the relationship between temperature and energy levels is primarily about occupancy changes rather than shifts in the energy levels themselves.
bananabandana
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Why is is true that for a given system, if I fix the volume and increase the temperature, you'd expect the occupancy of the energy levels to change, but not the levels themselves?

Can I think of this in terms of the fact that the boundary conditions for the solution of the TISE are fixed, such that we have the same form of solution? (and same density of states) Or is there some other explanation?

Thanks
 
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Can I think of this in terms of the fact that the boundary conditions for the solution of the TISE are fixed, such that we have the same form of solution?
Yes.

The energy levels depend on whatever goes into the SE, if temperature is not there, then the energy levels do not depend on temperature.
In thermodynamics, temperature is the mean velocity of the particles... this would be related to the energy levels how?
 

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