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In a book, I read that the wave function of a system should not become infinite in a finite region and also should vanish at infinity. For the first part I think that if wave function is infinite in finite region the normalization constant becomes zero due to which wave function vanishes. But I am not able to find the reason behind the vanishing of wave function at infinity. Please clarify this doubt.

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    $\begingroup$ It's a boundary condition. $\endgroup$ – Todd Minehardt Apr 18 '20 at 17:45
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    $\begingroup$ because the wavefunction integral must evaluate to 1, a finite value at infinity cannot sum to 1 $\endgroup$ – Cody Aldaz Apr 18 '20 at 17:46

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