let us consider the SchrΓΆdinger equation with potential V(x)=U(x)+iW(x):
iββtβΟβ=β2mβ2ββ2Ο+(U(x)+iW(x))Ο(1)The conjugate equation
βiββtβΟββ=β2mβ2ββ2Οβ+(U(x)βiW(x))Οβ(2)After multiplying Eqn 1 by Οβ, Eqn 2 by Ο and subtracting, we get
iβ(βtβΟβΟβ+βtβΟββΟ)=
β2mβ2β(Οββ2ΟβΟβ2Οβ)+2iW(x)ΟΟβor
βtβΟβ+βjβΞ³Ο=0Here
Ο=ΟΟβ
j=2miββ(ΟββΟβΟβΟβ)
Ξ³=2W(x)/β
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