[hat car]

Can someone please tell me the steps to doing this

[Corribus]

Do you know what normalization means?

[hat car]

Yes I think anyway, normalizing a wave function means finding the form of the wave function that makes the statement
∫ Ψ* Ψdx=1 true, with the limits of integration -∞ to ∞. When you normalize a wavefunction you're essentially finding the exact form of Ψ which ensures the probability that the particle will be found somewhere in a space equal to 1.

Now I know that the limits of integration for the normalized wavefunction of a particle on a ring are 0 and 2π, I just don't know how to go about normalizing the wavefunction.

[Corribus]

What you are asking now is slightly different than what the thread title asks.

If you have a wavefunction and you want to show that it is normalized, you just need to perform the indicated integration and show that it is, indeed, equal to 1.

If you have a wavefunction that you need to normalize, you need to introduce a normalization factor to the wavefunction, often labeled "N", and then solve the equation for N.

E.g., if your (unnormalized) wavefunction is ψ, then call your normalized wavefunction Nψ. Then you need to solve the equation ∫N²ψ*ψ dτ = 1 for N. Note that if your wavefunction is already normalized, N will equal 1. Also note that I have used dτ to indicate that the dimension is not always "x", as in the case of the particle on the ring, which is integrated over angular space. Likewise, the limits of integration are not always -∞ to ∞. (It doesn't make sense, for example, to intregrate over angles ranging from -∞ to ∞. The integration in this case is usually 0 to 2π, which is the full range of angles around a circle.)

If you need help performing an integration, this is more of a math problem than anything else. You can find help here, but you have to first specify the actual wavefunction you are trying to normalize.

[Big-Daddy]

How far have you got with the problem? If you have the un-normalized wave-function, then multiply it by normalization constant N, write ψ·ψ*, and then integrate over θ from 0 to 2pi (I assume you are in polars) as the wave-function is periodic in θ with a period 2pi.

N comes out quite neatly. It is, as Corribus said, a pure-maths question.

[Enthalpy]

Could the diffiiculty result from the integration variable?

If ψ is a function of xyz then one integrates |ψ|² for all x, y, z.
Sometimes ψ varies only with x, then x and y are omitted AND ψ is re-written as a density versus x only, but this explanation is usully omitted. Because of it, just |ψ|² integrated over x must be normalized.

Over a ring, ψ is often modelled as a toroid, and since its phase is to vary only with the angle, ψ is already integrated over the polar direction and the radius, to give a function of the angle only, which is written ψ as well despite being a different function. Then, integrating over the angle does the rest to check or make the normalization.

The linear algebra behind tells that wavefunction can be written over many bases. ψ can be written as a function of the 3D position (=a weighed sum of Dirac of all possible positions), or just as well as a function (=a weighed sum) of all momenta, and then the normalization means to integrate over all the momenta instead. And sometimes the wavefunction combines a limited set of possibilities, like the energies of a trapped particle; in such a case, when the wavefunction is a linear combination of all eigenfunctions, the normalization is more easily done by integrating over a discrete set of values, that are the scalar contributions of all the eigenfunctions.