Is ψ(x) = A/(x - ik) a Valid Wave Function?

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SUMMARY

The wave function ψ(x) = A/(x - ik) is not a valid wave function due to its discontinuity at x = ik, where k is a constant and i represents the imaginary unit. A valid wave function must be continuous and defined for all real numbers within the interval from -∞ to ∞. The mathematical condition for a wave function to be valid includes continuity and normalization, which this function fails to meet due to the singularity at x = ik.

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mclame22
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ψ(x) = A/(x - ik) over the region x = -∞ to ∞

A and k are constants, and i is √-1. I'm not sure if this is a valid wave function or not. I know that ψ must be continuous "everywhere," but this function does not exist for x = ik. But x only takes on the form of real numbers over the interval -∞ to ∞. Any help is greatly appreciated.
 
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What's the mathematical condition for a wavefunction to be valid ? Please, search your notes for this.
 

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