What is the Frequency of a State Function Describing a Proton?

[Jelfish]

I have this state function that I've gotten to the form:

$$\Psi = A*\exp[iE_1 t/h] + B*\exp[4iE_1 t/h]$$

where A and B are functions of x. I know the energy. The h's are h-bars.

The state function is suppose to describe a proton and I'm asked to find the frequency.

My first thought is to somehow combine the terms such that I would have something like

$$\Psi = C*\exp[i\omega t]$$

Where $$\omega$$ would be the angular frequency.

I'm having some trouble trying to get it to this form.

What I want to know is if this is the correct approach.

Let me know if I need to give any more info. Thanks in advance.

 

[Jelfish]

If it matters, A and B are trig functions, cos(Pi x / L) and sin(2 Pi x / L) respectively, both times sqrt(2/L).

 

[Hurkyl]

Well, it helps to know the definition.

What you need to do is to find a period of your function -- that is, the smallest positive constant H such that Ψ(t) = Ψ(t + H). (For all t) Then, the period is just the reciprocal of that.

 

[Jelfish]

Thanks! I'll try that.