In working out the derivation of the probability current density, I see (based on the definition of j(x,t)) that the limits of integration are changed from(adsbygoogle = window.adsbygoogle || []).push({});

d/dt∫(b to a) P(x.t) dx = iħ/2m[ψ*(x.t)∂/∂xψ(x.t) - ψ(x.t)∂/∂xψ*(x.t)](b to a)

to

d/dt∫(b to a) P(x.t) dx = -iħ/2m[ψ*(x.t)∂/∂xψ(x.t) - ψ(x.t)∂/∂xψ*(x.t)](a to b)

Thus, the prefactor becomes -iħ/2m as a result of reversing the limits of integration.

Is there a reason that the prefactor must be in terms of -i?

Thanks

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# Reversal of limits of integration in the derivation of probability current density

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