Particle in a box with non-flat bottom

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SUMMARY

The discussion focuses on the quantum mechanics problem of a particle in a box with a non-flat bottom. The user successfully demonstrated that all first-order energy shifts are zero, indicating that perturbation theory is applicable under specific conditions. The user seeks clarification on the constraints for the perturbation theory, specifically emphasizing that the parameter W must be small, which is a critical requirement for the method's validity.

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  • Understanding of quantum mechanics principles, particularly perturbation theory.
  • Familiarity with the concept of energy shifts in quantum systems.
  • Knowledge of boundary conditions in quantum mechanics.
  • Basic mathematical skills for solving differential equations related to quantum states.
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  • Research the implications of small perturbations in quantum mechanics.
  • Study the mathematical derivation of first-order energy shifts in quantum systems.
  • Explore the conditions under which perturbation theory is valid.
  • Learn about the application of perturbation theory to systems with non-standard boundary conditions.
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Students and professionals in physics, particularly those studying quantum mechanics and perturbation theory, as well as educators seeking to explain these concepts effectively.

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Homework Statement



please see q attached..


Homework Equations





The Attempt at a Solution



Ok so I've shown that all the first order energy shifts are zero. I'm just not sure what the simple explanation for this is...?


THanks!
 

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also - another question says: discuss the constrains on W for perturbation theory to be asuitable approx method.

What can i say beyond W must be small? anything else..?

Thanks
 

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