text: ## Solve two eigenfunctins for a Finite Square Well
  
  1. The problem statement, all variables and given/known data
  
  Solve Explicitly the first two eigenfunctions ψ(x) for the finite square wave potential V=V0 for x<a/2 or x>a/2, and V=0 for -a/2<x<a/2, with 0<E<V0.
  
  2. Relevant equations
  
  See image
  
  3. The attempt at a solution
  
  See image. After modeling an in class example, my classmates and i were stuck here. We have 5 unknowns, and 4 conditions. We know we have integrate the square of each region (as shown) and add to normalize and solve this, but we don't know how to handle/solve for the unknowns
  
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   Recognitions: Gold Member First you must do those integrals to give yourself the final condition. Then you will have five equations, two from each matching point, and the normalization condition. After, its a matter of solving 5 equations and 5 unknowns. If you feel comfortable, use mathematica, if not, do it by hand. Methods of substitution or elimination can get it done.
  
   Quote by jfy4 First you must do those integrals to give yourself the final condition.
  Which lines should be integrated? The ones for the 3 regions or the 4 conditions? Im unclear on how i will be getting 5 equations.
  
  And I presume that you are saying to integrate first, and then solve for the unknowns?
  
  Recognitions:
  Gold Member
  Homework Help
  Staff Emeritus
  
  ## Solve two eigenfunctins for a Finite Square Well
  
  The five equations are the two you wrote down for x=a/2, the two you wrote down for x=-a/2, and the normalization condition.
  
  You should recheck your work. There are a few errors in your equations.
  
  Add the first and third equations together, and add the second and fourth equations together. Then divide one result by the other. You should get something like
  $$\beta \tan (\beta a/2) = \alpha$$ (or maybe cot instead of tan). You should be able to show that for this to hold, either C or D has to vanish.
  
   Tags eigenfunction, energy, square well
explanation: The document describes a physics problem related to solving the first two eigenfunctions for a finite square well potential. It includes a problem statement, relevant equations, and an attempt at a solution. The text also contains a discussion between two individuals, one of whom is providing guidance on how to proceed with the problem. The document contains a question and an answer.
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distilabel_metadata.content: ## Solve two eigenfunctins for a Finite Square Well
  
  1. The problem statement, all variables and given/known data
  
  Solve Explicitly the first two eigenfunctions ψ(x) for the finite square wave potential V=V0 for x<a/2 or x>a/2, and V=0 for -a/2<x<a/2, with 0<E<V0.
  
  2. Relevant equations
  
  See image
  
  3. The attempt at a solution
  
  See image. After modeling an in class example, my classmates and i were stuck here. We have 5 unknowns, and 4 conditions. We know we have integrate the square of each region (as shown) and add to normalize and solve this, but we don't know how to handle/solve for the unknowns
  
   PhysOrg.com science news on PhysOrg.com >> Hong Kong launches first electric taxis>> Morocco to harness the wind in energy hunt>> Galaxy's Ring of Fire
   Recognitions: Gold Member First you must do those integrals to give yourself the final condition. Then you will have five equations, two from each matching point, and the normalization condition. After, its a matter of solving 5 equations and 5 unknowns. If you feel comfortable, use mathematica, if not, do it by hand. Methods of substitution or elimination can get it done.
  
   Quote by jfy4 First you must do those integrals to give yourself the final condition.
  Which lines should be integrated? The ones for the 3 regions or the 4 conditions? Im unclear on how i will be getting 5 equations.
  
  And I presume that you are saying to integrate first, and then solve for the unknowns?
  
  Recognitions:
  Gold Member
  Homework Help
  Staff Emeritus
  
  ## Solve two eigenfunctins for a Finite Square Well
  
  The five equations are the two you wrote down for x=a/2, the two you wrote down for x=-a/2, and the normalization condition.
  
  You should recheck your work. There are a few errors in your equations.
  
  Add the first and third equations together, and add the second and fourth equations together. Then divide one result by the other. You should get something like
  $$\beta \tan (\beta a/2) = \alpha$$ (or maybe cot instead of tan). You should be able to show that for this to hold, either C or D has to vanish.
  
   Tags eigenfunction, energy, square well
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distilabel_metadata.raw_output_q_a_detector_0: The document describes a physics problem related to solving the first two eigenfunctions for a finite square well potential. It includes a problem statement, relevant equations, and an attempt at a solution. The text also contains a discussion between two individuals, one of whom is providing guidance on how to proceed with the problem. The document contains a question and an answer.
  
  Label: question-and-answer