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I have been able to figure out the first half of the problem described below in the image. The part I am struggling on is finding the $C$ constant such that it will lead to a normalized solution of $\psi$. My understanding of normalizing a constant is that if you integrate it from $-\infty$ to $\infty$, you should get one. I have tried integrating this function but I can't seem to get a numerical value for $C$. My instructor insists there is no integration necessary and all that I need to do is look at the relation that $\psi = -2\ln(Z)$ in order to find $C$ but I can't seem to figure out what he means by this. Any tips would be very helpful.

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joy
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Battler
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  • I think by "normalized" he just means that $\Vert \psi(\cdot,t)\Vert_1$ is finite for all $t$. – K.defaoite Nov 15 '22 at 16:24
  • Maybe the point is that, if you want $\psi$ to be normalizable, its limit as $x$ goes to positive and negative infinity must not be a finite constant. – Elliot Yu Nov 15 '22 at 17:02

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