Show that a wave function is correctly normalised?

[Dream_Theater]

Hi, could someone please tell me how I would show that a wave function is correctly normalised?

I know to integrate the square of the function between infinity and negative infinity, but is the complex conjugate required?

Any help is much appreciated :D

 

[Avodyne]

You integrate the absolute square of the wave function, which is the wave function times its complex conjugate.

 

[Dream_Theater]

Thanks, that helps a lot. I can see where I was going wrong.

Also, for a wavefunction, can the expectation value of the position be equal to zero?

 

[jtbell]

It means that the particle is equally likely to be found on one side of the origin of your coordinate system, as on the opposite side. Whether that's possible or not depends on the situation. For a hydrogen atom in the ground state, with the proton at the origin, <x> for the electron is in fact zero. For the classic textbook particle in an "infinite square well" whose boundaries are at x = 0 and x = L, <x>= 0 is not possible.

 

[Dream_Theater]

Thanks, that really helps. I was wondering because I was looking at a question that didn't really specify the conditions. I'll check through my working and see if I've made any mistakes. Also, if <x> is zero, can <p> also be zero?