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SWE Solutions' General Form

  1. Nov 1, 2009 #1
    I'm learning how to solve the Schrodinger wave equation and I know that the solutions are of the general form:

    [tex]\Psi[/tex](x) = A sin kx + B cos kx

    This was given to us, but where did it come from? Is it the fact that the wave could be a sine or cosine wave, and the other constant multiplier (A or B) can then be set to zero using boundary conditions? Or is there something more complicated going on here?
     
  2. jcsd
  3. Nov 2, 2009 #2
    Hi.
    ψ (x) = A sin kx + B cos kx
    is derived from
    ψ" (x) = -k^2 ψ (x)
    which is derived from
    (-i hbar ∂/∂x)^2/2m ψ (x) = hbar^2 k^2/2m ψ (x)
    which is stationary SWE in the system of no potential energy with energy eigenvalue hbar^2 k^2/2m.
    A and B are chosen to meet the boundary conditions.
    Regards.
     
  4. Nov 2, 2009 #3
    Ooooookay, that makes sense. I wasn't sure where (or even if) -k^2 came into play here, but now that you showed me, I should have seen it. I didn't even think of reducing h, but that makes a lot more sense. Thanks a lot for the response.
     
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