Solve coefficients for four equations in square well

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Homework Help Overview

The discussion revolves around solving for coefficients A, B, I, and J from a set of four equations related to a square well problem in physics. The equations involve relationships between these coefficients and are presented in a linear system format.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the challenge of having five unknowns with only four equations, suggesting that one can express four coefficients in terms of the fifth. There are attempts to solve the last two equations for I and J in terms of D, and then substitute these into the first two equations to find A and B. Some participants express confusion about the algebra involved and the implications of solving for I and J.

Discussion Status

The discussion is ongoing, with participants exploring various approaches to manipulate the equations. Some guidance has been offered regarding solving for coefficients in terms of others, but there is no explicit consensus on a single method. Participants are actively questioning their understanding of the relationships between the variables and the algebraic steps needed to progress.

Contextual Notes

There is mention of difficulties with LaTeX formatting in posts, which may affect the clarity of the equations presented. Additionally, the participants are navigating the complexity of multiple variables and equations, which is contributing to their confusion.

dsdelavega

Homework Statement


Hello, I am stuck on four equations for which I must find the coefficients A,B,I,J.
I have tried using latex but the commands don't seem to work.

Homework Equations


Four equations:

[tex]A+B = I+J[/tex]
[tex]\frac{\alpha}{k}(J-I) = A - B[/tex]
[tex]D = Ie^{ia(\alpha-k)} + Je^{-ia(\alpha + k)}[/tex]
[tex]D = -\frac{\alpha}{k}Ie^{ia(\alpha-k)} - \frac{\alpha}{k}Je^{-ia(\alpha + k)}[/tex]

The Attempt at a Solution


I = [2B + J((alpha/k)-1)]/ (1+ (alpha/k))

i got this from setting 1 and 2 equal to A then solving for I but i don't know where to go from here. Any tips?
 
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You have five unknowns, A, B, D, I, and J, but only four equations. You can solve for four of the coefficients in terms of the other one.

I'd solve the last two equations for I and J in terms of D. Then once you have those, plug the results into the first two equations and solve for A and B.
 
vela said:
You have five unknowns, A, B, D, I, and J, but only four equations. You can solve for four of the coefficients in terms of the other one.

I'd solve the last two equations for I and J in terms of D. Then once you have those, plug the results into the first two equations and solve for A and B.

Yes, we were told that we should solve in terms of our incident wave direction which is the value B in this case.
So if i solve for I and J in terms of D does that mean just set 3 = 4 and solve for I and J?
 
These are linear systems of equations, like x+y=2 and x-y=1. You solve them the same way.
 
vela said:
These are linear systems of equations, like x+y=2 and x-y=1. You solve them the same way.

I understand, I am just getting lost in the algebra trying to match terms.
Also, any chance you can tell me how to implement the latex equations? I know how to use latex but i don't know how to do it on a post. thanks!

when setting 3 = 4 then I solve for I, then the result I get is the following:

[tex]I = J e^{-2ia\alpha} \frac {k-\alpha} {k+\alpha}[/tex]

I don't know what to do after this.
The four equations are throwing me off because of the many variables.
Additionally,I can't plug this into equation 1 because I wouldn't know what A is.
 

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