I am having a problem with an example problem in my physics book. The example goes like so:
[tex]\psi(x) = Ax + B[/tex]
[tex] A, B, constant [/tex]
is a solution of the Schrodinger equation for an E = 0 energy level of a particle in a box. b.) what constraints do the boundary conditions at x = 0 and x = L place on the constants A and B?
The Attempt at a Solution
Part a i understand completely -- i just take the second derivative of the wave function and find its eigenvalue to be 0, which corresponds to the energy. However, for part b, I am not quite understanding how the book applies the boundary conditions. They claim the following:
"applying the boundary condition:
[tex] x = 0[/tex]
[tex]\psi(0) = A = 0[/tex]
[tex] A = 0, and \psi(x) = Bx[/tex].
Then applying the boundary condition:
[tex] x = L[/tex]
gives [tex] \psi(L) = BL = 0[/tex]
so B must be zero. How are they finding this for the IVP? If i plug zero into the wave function i get B = 0, not A = 0. I must be missing something. Could someone please tell me what I'm not seeing? Thank you!