A question in one dimensional Schroedinger Equation.

[Karmerlo]

I read something like this:

since U(x)(the potential field) is a real,ψ and ψ^* can both be the solution of Schroedinger Equation.I cannot understand this. Anyone can give me an explanation.

Thanks.

 

[Fredrik]

I wrote something else here earlier, but I think what i said is wrong. A solution of the Schrödinger equation satisfies $$\psi(x,t)=e^{-iHt}\psi(x,0).$$ This implies $$\psi(x,t)^*=e^{iHt}\psi(x,0)^*.$$ So the complex conjugate is only a solution if we reverse the direction of time.

A tip for next time is that you include a reference to where you saw the statement, if possible with a link to the correct page at Google Books.

 

[Bill_K]

The time-independent Schrödinger equation is (-h²/2m) ψ(x) + U(x) ψ(x) = E ψ(x).
Take the complex conjugate of this equation, and since U and E are real, you get
(-h²/2m) ψ*(x) + U(x) ψ*(x) = E ψ*(x)
showing that ψ*(x) satisfies the same equation.