- #1
hnicholls
- 49
- 1
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
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
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