Why is a QM wave function not normalizable

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SUMMARY

A wave function in quantum mechanics is not normalizable if its second derivative maintains a consistent sign, indicating that the function curves away from the x-axis. Specifically, in one-dimensional space, if the ratio f"/f is positive, the wave function cannot approach zero, which is necessary for normalizability. The discussion highlights the misconception of applying real-number comparisons to complex-valued wave functions, emphasizing that the presence of a nonzero imaginary part complicates the interpretation of positivity.

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Ed Quanta
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In quantum mechanics, why is a wave function not normalizable if it always has the same sign as its second derivative?
 
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In 1D, if f"/f is positive, the function curves away from the x axis.
To be normalizable, it must in some region curve toward the x axis.
 
Ed Quanta said:
In quantum mechanics, why is a wave function not normalizable if it always has the same sign as its second derivative?

Your question doesn't make (too much) sense, since a wave function is a complex (generally with a nonzero imaginary part) valued function and to say that [itex]a+ib >0[/itex] makes no sense.
 

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