Eigenvalue Question (p2.14 in Quantum Chemistry and Spectroscopy)

[anduril66]

function: e^-(x^2/2)
operator: d^2/dx^2 -x^2

The answer key says the function is an eigenfunction of the operator with an eigenvalue of -6.

I can't figure out how to reach this conclusion. Also, Wolfram Alpha says d/dx(d/(dx)e^(-x^2/2)) = e^(-x^2/2) (x^2-1). Isn't this inconsistent with the answer key? Thanks.

 

[ehild]

It is an eigenfunction, but with different eigenvalue.

ehild

 

[peeeeeb]

guys please help me doing this,
the operator is given as x+ d/dx
i have to find the eigenvalue. how to do it?