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I'm trying to calculate the probability for a particle to penetrate a potential well. The problem is that to calculate this, one must solve an equation system that becomes to big. I tried solving it using a matrix and inverting that, but half way, the matrix didn't even fit on my computer screen...

These are the equations:

[tex]e^{ika} + Re^{-ika} = Ae^{ima} + Be^{-ima}[/tex]

[tex]Te^{ikb} = Ae^{imb} + Be^{-imb}[/tex]

[tex]ke^{ika} - Rkae^{-ika} = mAe^{ima} - mBe^{-ima}[/tex]

[tex]kTe^{ikb} = imAe^{imb} - mBe^{-imb}[/tex]

I tried substituting some common parts, but that didn't help much. How can I solve this? What method should I use?

Thanks in advance,

Nille