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How to systematically solve an underdetermined matrix

Hello!

I am trying to solve The Schrodinger Equation(s) for a finite walled double potential barrier, and in order to find the transmission coefficient I need to find the coefficients of the Wave Equations as ratios of one another (since this is all we can do..since it is underdetermined). I have nine equations and eight unknowns, all set up in a massive 9x8 matrix. Since all the terms in the matrix are constants, it seems like this would be straightforward...however it is quite hellish.

So, my question: Is there a program out there that can solve an underdetermined matrix of coefficients in terms of ratios of one another? I'm thinking MatLab could probably do it, however I haven't used that program in ages so I wouldn't know where to begin. Thanks!

IHateMayonnaise
 

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