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Eigenvalue problem

  1. Mar 26, 2008 #1
    1. The problem statement, all variables and given/known data
    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. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Mar 26, 2008 #2


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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?
  4. Mar 26, 2008 #3
    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
  5. Mar 26, 2008 #4


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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??
  6. Mar 26, 2008 #5
    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.??
  7. Mar 26, 2008 #6
    i see. c=2c(abx2-2bx+2a2) . But still I don't found value of a and b. May be problem is me :)
  8. Mar 26, 2008 #7


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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: Mar 26, 2008
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