Unable to state a simple square-well Schrödinger problem: "This system cannot be solved"

[gustaf (Christer Gustafsson)]

Dear all,

Below is my Mathematica code I hoped should represent a standard problem in first-year quantum mechanics: a particle passes over a 1D potential well and the (wave) gets both transmitted (T) and and reflected (R). In addition the phases of the two waves are of interest. Boundary conditions are imposed and these lead to four (real) equations in the four unknowns. Text books (e.g. Merzbacher “Quantum Mechanics”) leave the solution as a student’s exercise. It is therefore bitter, now sixty years later, not to be able to formulate the problem in a proper way for Mathematica because Solve says it cannot solve such a problem.

Hopefully someone can point out what is my error! The small m-file err3.m is attached.

Best regards,

ChG

P.S. The code outputs a LaTeX-file. I have left it as-is

err3.m (1.72 KB)

[alamkhan1909 (Alam Khan)]

Dear Christer,

Mathematica 12.0 can solve the system of the equations. I am getting the following solution:

I hope that this solves your problem.

Best,
Alam

[gustaf (Christer Gustafsson)]

Thank you Alam,

After I removed $Assumptions, then my err3.m also solves the equation system.

Best regards,

Christer