That looks like it works. Do you know where this comes from? I figured it involves the pauli matrices in each of two orthogonal directions acting on the possible wavefunctions, but I wasn't sure how to arrange that into an equation.
So in my quantum class we learned that if you measure spin in one direction and get h/2 and then in another direction that it will be (plus or minus)h/2 as well. I was wondering how you would know the probability of it being the positive value vs the negative value. It's a function of the...
The normalization condition is:
∫|ψ|^{2}d^{3}r=1
In spherical coordinates:
d^{3}r=r^{2}sinθdrdθd\phi
Separating variables:
∫|ψ|^{2}r^{2}sinθdrdθd\phi=∫|R|^{2}r^{2}dr∫|Y|^{2}sinθdθd\phi=1
The next step is the part I don't understand. It says:
∫^{∞}_{0}|R|^{2}r^{2}dr=1 and...
Homework Statement
I need to find the residue of \frac{e^{iz}}{(1+9z^{2})^{2}} so I can use it as part of the residue theorem for a problem.
Homework Equations
Laurent Series
R(z_{0}) = \frac{g(z_{0})}{h^{'}(z_{0})}
The Attempt at a Solution
I tried using the laurent series but...
Nevermind, you're right, I got it. All the other problems had us manipulate the bessel function as an infinite series and I was just used to doing this. Forgot to try basic rules from calculus...haha thanks
Homework Statement
Solve equations 1) and 2) for J_{p+1}(x) and J_{p-1}(x). Add and subtract these two equations to get 3) and 4).
Homework Equations
1) \frac{d}{dx}[x^{p}J_{p}(x)] = x^{p}J_{p-1}(x)
2) \frac{d}{dx}[x^{-p}J_{p}(x)] = -x^{-p}J_{p+1}(x)
3) J_{p-1}(x) + J_{p+1}(x) =...