Page13 on Griffiths quantum mechanics

[Frank0]

In the prove of the Schrödinger equation preserves the normalization I don't understand the step
from

∂ψ/∂t=ih/2m ∂2ψ/∂x2- i/h Vψ

to

∂ψ*/∂t=-ih/2m ∂2ψ/∂x2+ i/h Vψ* (h represents h bar)

the book says "taking complex conjugate equation" but I don't see how.

Thanks in advance.

 

[Elwin.Martin]

In the prove of the Schrödinger equation preserves the normalization I don't understand the step
from

∂ψ/∂t=ih/2m ∂2ψ/∂x2- i/h Vψ

to

∂ψ*/∂t=-ih/2m ∂2ψ/∂x2+ i/h Vψ* (h represents h bar)

the book says "taking complex conjugate equation" but I don't see how.

Thanks in advance.

Welcome Frank, it says it's your first post~

Alright so we literally just change any aspect of the equation which contains an imaginary component to minus said component.

For example...
e^{-iHt/ \hbar}
goes to

e^{iHt/ \hbar}

We make the assumption that V is real and that ψ is complex.

Given the above should help, I'm sure you're familiar but, just in case ψ* refers to the complex conjugate of ψ.

Let me know if I missed what you were asking some how, though I'm sure someone can answer a little more cleanly.

http://en.wikipedia.org/wiki/Complex_conjugate
The wiki page provides the general information on conjugating as well.

 

[The_Duck]

If you have some equation a = b then you can take the complex conjugate of both sides and get a* = b*. Then you just have to know that the complex conjugate of a product is the product of the complex conjugate; the complex conjugate of a derivative is the derivative of the complex conjugate; the complex conjugate of i is -i; etc.