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Given that the time dependent Schrodinger equation preserves the wavefunction normalization, does this mean that the time independent Schrodinger equation, i.e. φ(x), preserves this normalization criteria?

Given that the time dependent Schrodinger equation preserves the wavefunction normalization, does this mean that the time independent Schrodinger equation, i.e. φ(x), preserves this normalization criteria? Correct Answer No, because there is no position derivative or variables term that allows φ—→ 0 as x—→ ±∞.

The mathematics of normalization does not allow φ—→ 0 as x—→ ±∞ for solely a position derivative. This does not make the right-hand side of the time independent zero for any arbitrary wavefunction. Normalization criteria for the wavefunction is purely dependent on the wavefunction form itself.

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