Solving Eigenvalue Problem for Operator d2/dx2 - bx2, Function psi=e^-ax2

[quark16]

Homework Statement

operator is d2/dx2 - bx2
function is psi=e^-ax2

if this fuction is eigenfuction for this operator, what is "a" and "b" constants value?

Homework Equations

The Attempt at a Solution

 

[Dick]

Apply the operator to psi. Set what results to c*psi. Can you find a relation between a and b that makes c a constant?

 

[quark16]

this question is from Atkins physical chemistry. psi is not constant, it is just only wavefunction. Thank you for your attention, I really don't solve this question

 

[Dick]

Makes "c" a constant, not makes "psi" a constant. Start by applying the operator to the wavefunction psi. What do you get??

 

[quark16]

result is 2e^-ax2 (abx2-2bx+2a2). It is mean (abx2-2bx+2a2) is a constant. But this question want to value of a and b. I am confused.??

 

[quark16]

i see. c=2c(abx2-2bx+2a2) . But still I don't found value of a and b. May be problem is me :)

 

[Dick]

I get something pretty different for the value of the operator on psi. If you multiply it out shouldn't there be a -b*x^2*psi(x) part from the '-bx2' part of your operator? We'd better worry about getting the value of the operator right before we talk about eigenvalues. What's the second derivative of psi?