Phase Shifting Wave Functions: A How-To Guide

[SpaceTrekkie]

Homework Statement

Show that a wave function is phase-shifted by (pi)/2 when multiplied by
i and by (pi) when multiplied by −1.

Homework Equations

The wave function form I am using is function = A(cos(kx-wt)+isin(kx-wt))

But it was not specified which kind I can use

The Attempt at a Solution

I am not sure even where to begin...

 

[CompuChip]

I think this is not a physics question, just a mathematics one
Phase-shifting by $\phi$ means replacing $$\psi \to e^{i \phi} \psi$$ ($\phi$ is called the phase, because the phase factor exp(i phi) only changes the argument and not the modulus of psi, so physical quantities which generally depend on $|\psi|$ are not affected by such a change).
So basically what they want you to show, as far as I can tell, is that if you set phi = pi / 2 then that's the same as changing psi for i psi - which is mathematics, not physics; and very easy too.

 

[SpaceTrekkie]

Thanks, I actually manged to figure it out after I posted, thank goodness. Yeah, I guess that was actually math, but it was for my wave optics class which is physics 306 so I put it here :-)