Help Solve for the normalization constant of this QM integral

AI Thread Summary
The discussion centers on finding the normalization constant A for a given wavefunction, but the integral required for normalization does not converge, indicating the wavefunction is not normalizable and thus invalid. Participants note the inconsistency of this problem being included in a final exam, especially since subsequent questions suggested the wavefunction should be normalizable. There is speculation about a possible typo in the wavefunction, proposing an alternative form that aligns better with quantum mechanics principles. The issue raises concerns about the clarity and validity of exam questions. Overall, the integral's divergence highlights a fundamental problem with the wavefunction's applicability in quantum mechanics.
casparov
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Misplaced Homework Thread
Homework Statement
find A
Relevant Equations
psi = A exp [ - x^2 / (2+ix) ]
I'm given the wavefunction

ψ = A exp(-x^2/(2 + i x))


and I need to find the normalization constant A.

I believe that means to solve the integral

1/A^2 = integral_(-∞)^∞ e^(-x^2/(2 + i x)) e^(-x^2/(2 - i x)) dx


The question does give some standard results for the Gaussian function, also multiplied by x to some different powers in the integrand, but I can't seem to get it into that form.
Whatever I do, I get an x in the denominator of the exponent, and makes it impossible to solve for me.
 
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casparov said:
I'm given the wavefunction

View attachment 326989

and I need to find the normalization constant A.

I believe that means to solve the integral

View attachment 326990
That is correct. However, this integral does not converge, so the given wave function is not normalizable (hence not a valid wave function).
 
DrClaude said:
That is correct. However, this integral does not converge, so the given wave function is not normalizable (hence not a valid wave function).
Sorry for the misplacement, it was a question on a final exam. Seems super odd to give this when the follow up questions implied it was normalizable. Thank you very much. Contacted my professor
 
casparov said:
Sorry for the misplacement, it was a question on a final exam. Seems super odd to give this when the follow up questions implied it was normalizable. Thank you very much. Contacted my professor
Could it be a typo?
$$
\psi = A \exp \left(- \frac{x^2}{2} + i x \right)
$$
would make more sense from a quantum mechanical point of view.
 
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