- #1
andre220
- 75
- 1
Homework Statement
Consider a particle oscillating according to [itex]x(t) = a\cos(\omega t)[/itex]:
Find [itex]\rho(x)[/itex], the probability density to find particle at position [itex]x[/itex].
Compute [itex]\langle x\rangle[/itex], [itex]\langle x^2\rangle[/itex].
Homework Equations
So in general we know that [itex]\textrm{Prob} = \int f_X (x)\,dx[/itex]
Also that [itex]\langle x\rangle = \int x f(x)\,dx[/itex], where [itex]f(x)[/itex] is a PDF and
[itex]\langle x^2\rangle = \int x^2 f(x)\,dx[/itex].
The Attempt at a Solution
Ok so, I think I am just seriously overlooking something here. However, that being said I cannot think of a way to construct [itex]\rho(x)[/itex]. We do know that it should normalize to 1, but I can't seem to think of where to get started at.
Any help is appreciated, thank you.