Calculate the probability current density vector →j for the wave function : ψ=Ae−i(wt−kx).
From my very poor and beginner's understanding of probability density current it is :
d(ψψ∗)dt=iℏ2m[dψdxψ∗−dψ∗dxψ]
By applying the RHS of the above equation :
iℏ2m[−A2ikxe−i(ωt−kx)ei(ωt−kx)−A2ikxei(ωt−kx)e−i(ωt−kx)]
This gives :
−2iA2ikℏ2m=kℏA2m
This is not the correct answer. :( What have I done wrong ?
In the model workings instead of A in the complex conjugate of the wave function they have written A∗. Why is this necessary since A is likely to be a real number anyways ?
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