Consider 1D particle in a box and it’s given normalized wave function Psi = Nsin(bx) where v(x) = 0 outside the box and v(x) = cos(pix/L) inside the box from x = 0 to x = 1.   (a) show that the wave function is a valid solution to the Schrödinger equation and what value of b makes it valid? (b) derive the eigenvalue expression

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Consider 1D particle in a box and it’s given normalized wave function Psi = Nsin(bx) where v(x) = 0 outside the box and v(x) = cos(pix/L) inside the box from x = 0 to x = 1.

 

(a) show that the wave function is a valid solution to the Schrödinger equation and what value of b makes it valid?

(b) derive the eigenvalue expression

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