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If the wavefunction φ(x,t) is complex, is the probability density real?

If the wavefunction φ(x,t) is complex, is the probability density real? Correct Answer Yes, because probability density is a square and hence cannot be complex

φ*(x,t)φ(x,t) = = φ*(x)φ(x). The complex part of the wavefunction thus disappears and the probability density depends on position only. This system is referred to as being in stationary state.

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