Hi, I have learned the Dirac equation recently and I managed to solve it for a free particle (following Greiner book “relativistic quantum mechanics” and Paul Strange book “Relativistic Quantum Mechanics”). I was asked to solve the Dirac equation in the stationary frame for a free particle (no potential and zero momentum) and transform the solution to that of a free particle with momentum. I found the solution for this on page 157 of Greiner’s book.(adsbygoogle = window.adsbygoogle || []).push({});

Now I have to do the same thing but with a square potential well, starting by a stationary potential well (with the solutions given in Strange’s Chap 9 page 263-267, Greiner Chap 9 page 197-199) which I understand, and then solve the Dirac equation for the same square potential moving at a constant velocity let’s say in the x-direction and find the transformation for the two solutions. I really have no clue on how to solve the Dirac equation for a moving potential well. I think that I have to set the boundary conditions moving at a constant velocity but I am not sure what I should do next.

I know that the calculation is nasty for this problem, but all I am asking for is if anybody know the strategy to use in order to solve the Dirac equation for a moving potential well, give me as much references as you can, papers, books.

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# Dirac Equation for a moving square potential well

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