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It is required to be continuous in the following text:
The book's reason why wave functions are continuous (for finite V) is as follows. But for infinite V, ##\frac{\partial P}{\partial t}=\infty-\infty=## undefined, and so the reason that wave functions must be continuous is invalid.
Source: Quantum Physics 3rd ed. by Stephen Gasiorowicz, p. 48
The book's reason why wave functions are continuous (for finite V) is as follows. But for infinite V, ##\frac{\partial P}{\partial t}=\infty-\infty=## undefined, and so the reason that wave functions must be continuous is invalid.
Source: Quantum Physics 3rd ed. by Stephen Gasiorowicz, p. 48
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