Showing that a set of functions is orthonormal

[hellomister]

Homework Statement

(phi)n (theta)=(2*pi)^(-1/2) * e^i*n(theta) 0<=theta<=2pi
Show that the set of functions is orthonormal where n is an integer

Homework Equations

(phi)n (theta)=(2*pi)^(-1/2) * e^i*n(theta) 0<=theta<=2pi
Definition of orthonormal: functions are orthogonal and of unit length
Definition of orthogonality: integral psi i* psi j dTau=0

The Attempt at a Solution

At first i wasnt sure what it meant by unit length so i integrated the equation from 0 to 2pi

i got (-i*e^i*n*theta)/((root(2pi)) * n)

but i don't know how to evaluate to see if it is equal to 0.
And if by unit length it means normalize, do i need to normalize the equation first then integrate and see if its equal to 0?
thanks for any help in clearing this up.

EDIT: btw how do people show their equations with nice symbols and such?

 

[D H]

Homework Equations

(phi)n (theta)=(2*pi)^(-1/2) * e^i*n(theta) 0<=theta<=2pi
Definition of orthonormal: functions are orthogonal and of unit length
Definition of orthogonality: integral psi i* psi j dTau=0

That does not look like the correct definition of the inner product here. For one thing, there is no psi or tau mentioned. Even fixing that, this definition is problematic. I think you need to use this:

$$\phi_n\cdot\phi_m = \int_0^{2\pi} \phi_n(\theta)\phi_m(\theta)^*\,d\theta$$

where that φ_m(θ)^* means the complex conjugate of φ_m(θ).

EDIT: btw how do people show their equations with nice symbols and such?

We use this site's LaTeX facility. Hover your mouse over the inner product equation above and you will see the code used to generate that equation. Also see [thread=8997]this thread[/thread]. And of course google is your friend. There is lots of material on the web on LaTeX.