Statistical physics:boltzman distribution

AI Thread Summary
The discussion centers on the application of the Boltzmann distribution to a one-dimensional square well used to trap helium atoms at 20 K. Participants express confusion regarding the evaluation of energy levels since the square well lacks an analytic solution. However, it is clarified that while the square well does not have a simple analytic form, numerical methods or approximations can be employed to determine energy levels. The validity of using the Boltzmann distribution hinges on the energy levels being accessible and well-defined in the context of statistical mechanics. Ultimately, understanding the energy states is crucial for applying the Boltzmann distribution effectively in this scenario.
oddiseas
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Homework Statement



A square well of length L= 0.6 mm is to be used as a trap for He atoms at 20 K. Consider the values of some of the lowest energy levels of He atoms in a 1-D square well. Explain if it is valid to use the Boltzmann distribution in this situation

Homework Equations





The Attempt at a Solution



The square well has no analytic solution, so how am i supposed to evaluate the energy levels to see if i can use a boltzman distribution?
 
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oddiseas said:
The square well has no analytic solution.
... Thats not true.
 
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Thread 'Help with Time-Independent Perturbation Theory "Good" States Proof'

(Disclaimer: this is not a HW question. I am self-studying, and this felt like the type of question I've seen in this forum. If there is somewhere better for me to share this doubt, please let me know and I'll transfer it right away.) I am currently reviewing Chapter 7 of Introduction to QM by Griffiths. I have been stuck for an hour or so trying to understand the last paragraph of this proof (pls check the attached file). It claims that we can express Ψ_{γ}(0) as a linear combination of...
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