[philmccrevace]

Hello, everyone! I'm having a problem with a question in quantum mechanics :

The normalized wavefunctions for a particle confined to move on a circle are

?(?) = ?(1/2?) e^-im?

? = pi
?() = square root

m = 0, ±1, ±2, ±3...
? = greater than or equal to 0, and lesser or equal to 2?

The problem wants to know what ? is. My teacher says that the answer is ?, but I have no idea how to get to this. What I started to do was use e^ix = cos x + i sin x, but I do not know if I have to switch the sign because the i in the problem is negative. I'm very rusty on my calculus and I dont know very many integrals. Where do I begin?

[Yggdrasil]

Recall that cosine is an even function.  So for any angle, a:

cos (-a) = cos (a)

Sine is an odd function.  So for any angle, a:

sin (-a) = - sin (a)

[philmccrevace]

Okay so I plugged in e^-ix = cos x - i sin x, so when I set x = m?, I get:

?(?) = ?(1/2?) cos m? - i sin m?

Where should I go from here? I know the answer is pi, but how do I set it up to find it?

[Yggdrasil]

The question doesn't really make sense.  To find ?, you need to be given a value for ? and m.