Solving a set of equations for A/F

[Rupesh]

Hi all,

These set of equations are solved which appears in Quantum physics. I think after trying I reached very near the answer but I am missing it, unfortunately

Hope somebody can help.

Solve for A/F from these 4 set of equations

A + B = C + D

ik1A - ik1B = -k2C + k2D

Ce^(-k2L)+De^k2L = Fe^ik1L

-k2Ce^(-k2L) + k2De^k2L = ik1Fe^ik1L

 

[stapel]

Solve for A/F from these 4 set of equations

A + B = C + D

Subtract B from either side, like you learned back in beginning algebra. This will give you "A=".

ik1A - ik1B = -k2C + k2D

I'm not sure why you need this second equation, since you already have an expression for A...? But you'd solve this one just like you solved back in beginning algebra: add ik₁B to each side, and then divide through by ik₁.

Ce^(-k2L)+De^k2L = Fe^ik1L

-k2Ce^(-k2L) + k2De^k2L = ik1Fe^ik1L

For each of these equations, you can divide through to isolate F. This will give you two different expressions for F. To find an expression for A/F, divide either of the expressions for A by either of the expressions for F. (Since we don't have the "advanced math" context, we cannot help you pick whichever is the "right" choice of expression. We can only provide the simple algebra instructions.)

These set of equations are solved which appears in Quantum physics. I think after trying I reached very near the answer but I am missing it, unfortunately

Please reply showing your efforts so far. Thank you!