Finite Square Well: Bond States and Asymmetric Potential Wells

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SUMMARY

The discussion centers on the existence of bound states in asymmetric finite square wells compared to symmetric ones. It is established that while symmetric potential wells always possess bound state solutions, asymmetric wells do not guarantee this outcome. The participants highlight that for asymmetric potential wells, an explicit equation can be derived to determine the energies of bound states, confirming that at least one bound state exists under certain conditions.

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  • Understanding of quantum mechanics principles
  • Familiarity with potential wells and bound states
  • Knowledge of mathematical derivation of energy equations
  • Concept of symmetric vs. asymmetric potentials
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LagrangeEuler
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I am not sure how is it possible that asymetric potential well does not have bond states if ##E<U_1<U_2##. In symmetric case solution always exists. Why this is a case?
 
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LagrangeEuler said:
I am not sure how is it possible that asymetric potential well does not have bond states if ##E<U_1<U_2##. In symmetric case solution always exists. Why this is a case?
I may be misunderstanding the question here... The asymmetric finite square well does have bound state solutions.
 
But not always. Right? Symmetric square well always has bound state solution.
 
For square (asymmetric) potential well an explicit equation with respect to energies of bound states is not difficult to derive. The existence of at least one bound state follows from that equation almost immediately.
 

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