What is the equation to calculate the amount of bound states in a well

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SUMMARY

The equation to calculate the number of bound states in a finite square well is derived from quantum mechanics principles. Specifically, the number of bound states can be estimated using the well's depth and width, typically represented as V0 (depth) and L (width). The graphical method involves plotting the sine and cosine functions to find intersections, which represent the bound states. This approach emphasizes understanding the wave functions rather than merely applying a formula.

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  • Understanding of quantum mechanics principles
  • Familiarity with finite square well potential
  • Knowledge of wave functions and their properties
  • Ability to interpret graphical representations of functions
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  • Study the mathematical derivation of bound states in quantum wells
  • Learn about graphical methods for solving quantum mechanics problems
  • Explore the implications of well depth and width on bound state calculations
  • Investigate the differences between finite and infinite square wells
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Students and professionals in physics, particularly those focusing on quantum mechanics and potential wells, will benefit from this discussion.

lozzyjay
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Homework Statement




i have a finite square well and I have to calculate how many bound states exist in it. I have the depth and the width of the well but I cannot find an equation anywhere to help me calculate it?
 
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Do you know the graphical method to find bound states? Apply that, and think. It's not a plug and chug question.
 

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