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Eigenvalue problem

  • Thread starter quark16
  • Start date
4
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1. 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?


2. Homework Equations



3. The Attempt at a Solution
 

Answers and Replies

Dick
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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?
 
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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
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Makes "c" a constant, not makes "psi" a constant. Start by applying the operator to the wavefunction psi. What do you get??
 
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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.??
 
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i see. c=2c(abx2-2bx+2a2) . But still I don't found value of a and b. May be problem is me :)
 
Dick
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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?
 
Last edited:

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