I would like to know why there is a minus sign on the right-hand side of the Schrödinger's complex conjugate equation, whereas in the Schrödinger's equation there isn't. I know it is a simple question, but I don't know where this comes from. −ℏ22m∂2ψ∂x2+V(x)ψ=iℏ∂ψ∂t
−ℏ22m∂2ψ∗∂x2+V(x)ψ∗=−iℏ∂ψ∗∂t
Answer
It is the definition of complex number. Let's say
z=x+iy⇒z∗=x−iy
z=x−iy⇒z∗=x+iy
In simple words, you just have to change the sign of the Imaginary part. The thing is that ψ(x) it's a imaginary number, so it's conjugate it's just ψ∗(x). If you have the ψ(x) function, then you can change i→−i or in the oposite way.
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