Help Solve for the normalization constant of this QM integral

In summary, the conversation discusses finding the normalization constant for a given wavefunction. However, the integral required to calculate the normalization constant does not converge, indicating that the given wavefunction is not normalizable and therefore not a valid wavefunction. The person also questions whether it could be a typo in the given wavefunction, suggesting a different expression that would make more sense from a quantum mechanical perspective.
  • #1
casparov
29
6
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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  • #2
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).
 
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  • #3
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
 
  • #4
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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