- #1

trf5

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## Homework Statement

Indicate which of the following expressions yield eigenvalue equations and identify the eigenvalue.

a) d/dx (sin(∏x/2))

b) -i*hbar * ∂/∂x (sin(∏x/2))

c) ∂/∂x (e-x^2)

## The Attempt at a Solution

I know that if the wave equation yields an eigenvalue equation, it will give me the wave equation multiplied by the eigenvalue back. I calculated the derivatives:

a) 1/2∏cos(∏x/2)

b)(-i*hbar∏/2)(cos(∏x/2))

c) -2x

Because none of these give me back the original wave function, does that mean none of these are eigenvalue equations? I don't think my professor would give us a problem that asks to calculate the eigenvalues, where there are no eigenvalues. In parts A and B, the ∏x/2 is in both the question and the answer, but the sin changes to cosine when you take the derivative, so does that mean it is not an eigenfunction? Any help would be appreciated.