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EngageEngage

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## Homework Statement

I am having a problem with an example problem in my physics book. The example goes like so:

a.)Show that

[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?

## Homework Equations

[tex]\frac{-\hbar^{2}}{2m}\frac{d^{2}\psi(x)}{dx^{2}}= E\psi(x)[/tex]

## 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]

so,

[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!