What are the variables in determining energy levels for a finite potential well?

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SUMMARY

The energy levels for a finite potential well can be determined using the equations γ = k cot(-ka/2) for B=0 and γ = -k tan(-ka/2) for A=0. These equations involve the wave number k and the width of the potential well a. Understanding the relationship between these variables is crucial for solving problems related to quantum mechanics and potential wells.

PREREQUISITES
  • Understanding of quantum mechanics principles
  • Familiarity with potential wells in physics
  • Knowledge of wave functions and boundary conditions
  • Basic proficiency in trigonometric functions and their applications
NEXT STEPS
  • Study the derivation of the Schrödinger equation for finite potential wells
  • Learn about the significance of wave numbers in quantum mechanics
  • Explore the implications of boundary conditions on wave functions
  • Investigate the graphical representation of energy levels in potential wells
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Students and professionals in physics, particularly those focusing on quantum mechanics, as well as educators seeking to clarify concepts related to finite potential wells and energy levels.

mju4t
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Hi, I am trying to show that the energy levels for a finite potential well can be determined from these two equations[tex]\gamma[/tex] = kcot(-ka/2) for B=0 and [tex]\gamma[/tex] =-ktan(-ka/2) for A=0.

I think it has something to do with substituting in the value of k, but I'm not quite sure where to start...any help would be appreciated!

Thanks,
Alex
 
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