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

AI Thread Summary
The discussion centers on determining the eigenvalue of the function e^(-x^2/2) with respect to the operator d^2/dx^2 - x^2. The answer key claims the function is an eigenfunction with an eigenvalue of -6, but there is confusion regarding this conclusion, as calculations using Wolfram Alpha suggest a different result. Participants express difficulty in reconciling the answer key with their findings, indicating that the function is indeed an eigenfunction but may have a different eigenvalue. Additionally, another user seeks assistance in finding the eigenvalue for a different operator, x + d/dx. Clarification and further assistance are requested to resolve the discrepancies in eigenvalue calculations.
anduril66
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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.
 
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It is an eigenfunction, but with different eigenvalue.

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