Energy levels generally invariant under fixed V, changing T

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SUMMARY

The discussion centers on the principle that energy levels remain invariant when the volume is fixed and temperature is increased in a given system. Participants confirm that while occupancy of energy levels changes with temperature, the energy levels themselves do not shift due to fixed boundary conditions in the Time-Independent Schrödinger Equation (TISE). The relationship between temperature and energy levels is clarified, emphasizing that temperature influences particle velocity but does not alter the fundamental energy levels defined by the Schrödinger Equation.

PREREQUISITES
  • Understanding of the Time-Independent Schrödinger Equation (TISE)
  • Basic principles of thermodynamics
  • Knowledge of quantum mechanics and energy level occupancy
  • Familiarity with boundary conditions in quantum systems
NEXT STEPS
  • Research the implications of boundary conditions on quantum systems
  • Study the relationship between temperature and particle velocity in thermodynamics
  • Explore the concept of density of states in quantum mechanics
  • Learn about the effects of temperature on occupancy of energy levels
USEFUL FOR

Students and professionals in physics, particularly those focusing on quantum mechanics and thermodynamics, as well as researchers interested in the behavior of energy levels in fixed volume systems.

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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