Symmetry in Physics: Wave Functions & e^i (Δ)

[bjon-07]

well my question was this...I was reading about symmetry in physics...feymann was talking about the wave function...if you have two identcal particles in different places...and find there wave functions...blah blah blah...the he mutiplied one of the wave fuctions by a factor of e^i (delta sign).

where did the e^i (delta) come from?

and what happens if the delta happens to be pi (e^i(pi))=-1



Sorry if this positive doesn't make any sense I am a hurry right now. but I can re-write it late if needed

 

[dextercioby]

Pure states in quantum mechanics are described by unit rays in the separable Hilbert space of states (for simplicity,only discrete spectra of observables).$\psi$ and $C\psi$ describe the same pure quantum state,as long as $|C|=1$,with $C\in\mathbb{C}$.

Daniel.

 

[selfAdjoint]

Pure states in quantum mechanics are described by unit rays in the separable Hilbert space of states (for simplicity,only discrete spectra of observables).$\psi$ and $C\psi$ describe the same pure quantum state,as long as $|C|=1$,with $C\in\mathbb{C}$.

Daniel.

and when a complex number c has norm 1 it lies on the unit circle in the complex plane, which is parametrized by the reals mod pi: $$c = e^{i\theta} = cos \theta + i sin \theta$$. Basic result in complex variables.

 

[James Jackson]

To further expand, you should realize that (assuming the states are normalised)

$$e^{i\theta}(|a\rangle +|b\rangle )\neq |a\rangle +e^{i\theta} |b\rangle$$

Where $e^{i\theta}\neq 1$It's all about relative phase...