Kinetic energy in a finite square well potential

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SUMMARY

The discussion centers on the comparison of average kinetic energy for a particle in a harmonic oscillator potential versus a finite square well potential. It is established that the average kinetic energy is influenced by the size of the potential, which acts as a variable parameter. Adjusting the size of the potential adiabatically can lead to equivalent average kinetic energies in both scenarios. The conclusion emphasizes the dependency of kinetic energy on the specific characteristics of the potential well.

PREREQUISITES
  • Understanding of quantum mechanics principles, specifically potential wells.
  • Familiarity with harmonic oscillator models in quantum physics.
  • Knowledge of adiabatic processes in quantum systems.
  • Basic grasp of kinetic energy calculations in quantum mechanics.
NEXT STEPS
  • Study the mathematical formulation of kinetic energy in quantum mechanics.
  • Explore the properties of finite square well potentials in quantum physics.
  • Learn about adiabatic processes and their implications in quantum systems.
  • Investigate the differences between harmonic oscillators and finite square wells in terms of energy states.
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Students and professionals in physics, particularly those focusing on quantum mechanics, as well as educators seeking to deepen their understanding of potential wells and kinetic energy concepts.

Moneer81
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Hello,

I have a quick question: While working on a problem involving a particle in a harmonic oscillator potential, I had to compute the average kinetic energy at t=0. My question is: would that average kinetic energy be the same or different if the particle was in the same state, but in a finite square well potential?
Thanks
 
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Hello,

This seems an undefinite question. The kinetic energy of the particle in some potential depends on the size of the potential, i.e. the size of the potential is a parameter that one can change and hence one change the kinetic energy. Therefore, one can adjust the size of the potentail slowly( or adiabatically) to reach that kinetic energy is the same. It's my opinion only.
Goodluck.
 

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