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## Homework Statement

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.

So,

[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]

and

[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?

## Homework Equations

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## The Attempt at a Solution

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