## 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
The text passage describes a physics problem involving solving for the first two eigenfunctions of a finite square well potential. It includes a problem statement, relevant equations, and an attempt at a solution, with a discussion on solving for unknowns using integrals and normalization conditions.
no_question

the passage does not contain a direct mathematical question or a specific calculation request. instead, it is a discussion of a physics problem and the steps required to solve it, including the need to perform certain integrations and solve a system of equations.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
## 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
user
The text passage describes a physics problem involving solving for the first two eigenfunctions of a finite square well potential. It includes a problem statement, relevant equations, and an attempt at a solution, with a discussion on solving for unknowns using integrals and normalization conditions.

TYPE: NO_QUESTION

The passage does not contain a direct mathematical question or a specific calculation request. Instead, it is a discussion of a physics problem and the steps required to solve it, including the need to perform certain integrations and solve a system of equations.