Quantum mechanics potential well solutions-help

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SUMMARY

The discussion focuses on solving potential well barrier equations in quantum mechanics, specifically deriving the coefficients A, B, C, D, and F from given conditions. The method involves systematically eliminating coefficients through substitution, starting with four equations for five unknowns to ultimately derive the ratio (A/B)^2. This algebraic approach requires careful manipulation of equations to backtrack and find all coefficients. Participants emphasize the importance of a structured method to simplify the problem-solving process.

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  • Understanding of quantum mechanics concepts, particularly potential wells
  • Familiarity with algebraic manipulation and substitution techniques
  • Knowledge of solving systems of equations
  • Basic grasp of quantum mechanics terminology, including coefficients and boundary conditions
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  • Study the derivation of potential well solutions in quantum mechanics
  • Learn about boundary conditions and their role in quantum systems
  • Explore algebraic techniques for solving systems of equations
  • Investigate the implications of coefficient ratios in quantum mechanics
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Students and researchers in physics, particularly those focusing on quantum mechanics and mathematical methods in physics, will benefit from this discussion.

asj23
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I was working through the textbook and it just gave the solutions to the potential well barrier as in [B/A]*2 and [F/A]*2 and T i was trying to figure it out with the conditions but couldn't get the answer i have attached the conditions, can some one show me how to find these values from the conditions

thanks
Andrew
 

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Show us what you've tried so far and maybe someone will be able to get you unstuck.

The basic idea is to eliminate the coefficients one at a time. You have four equations for five unknown coefficients A, B, C, D, F. First, you eliminate one coefficient by substituting equations into each other until you end up with three equations for four unknown coefficients. Then you eliminate another coefficient to get two equations for three unknown coefficients. Finally you get to one equation for, say, A and B, and that gives you (A/B)^2.

Then you backtrack and find the other coefficients. It takes a lot of algebra!
 

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