I have an infinite square well and I am asked to show why E = 0 and E < 0 does not satisfy the Schrodinger's equation. I must do this by applying the boundary conditions.
For E = 0:
I argued that the second derivative of the wave function is zero.
[tex]\Psi(x) = A + Bx[/tex]
By imposing the boundary conditions [tex]\Psi (0) = \Psi (a) = 0[/tex] I get:
[tex]\Psi(x) = Bx[/tex]
[tex]\Psi (a) = Ba = 0[/tex]
Therefore I concluded that:
(1) [tex]B[/tex] cannot be zero, or else we get [tex]\Psi(x) = 0[/tex] which is physically unacceptable
(2) [tex]a\neq0[/tex] since [tex]a[/tex] is the upper bound.
Perhaps before presenting my second solution to E < 0 I should make sure all the above is correct.
Is it valid?
The Attempt at a Solution