# Neutral particle with spin +1/2

1. Mar 23, 2017

### Fips

1. The problem statement, all variables and given/known data
Considering a neutral particle with spin +½ and a dipolar momentum μ placed on an uniform magnetic field. Find the variation of the expected value of the 3 cartesian components of the angular momentum spin operator for the following situations:

a) the angular momentum of spin is alligned with the magnetic field
b) the angular momentum of spin is perpendicular with the magnetic field

2. Relevant equations
∫ < Ψ | Sx | Ψ* > dx = < Sx >, Sx = ½hσ, σ is the matrix associated, spin +½ = (1 0)

3. The attempt at a solution
I thought if i calculated the integral to get the expected value and then use the heisenberg principle I could solve the problem. I figured i had to multiply the wave function with a spinor, since schrodinger's equation doesn't include spin. But I had no wave function so that's a no go.

2nd method was to only consider the angular difference given by the solid angle. Again with heisenberg's uncertainty principle, I'd get the variation of the expected value... thing is I have no clue on how I can proceed to calculate it in this way, is it just to say that θ = π and so it gets Φ=h/4? I don't think so :\

I could use apply dirac's method?

2. Mar 29, 2017

### PF_Help_Bot

Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.

3. Mar 30, 2017

### Staff: Mentor

Since you are dealing with spin, using wave functions is not the best approach. You should try working with the Dirac notation or using a matrix-vector notation.

Also, the point in not find the angle of the spin (which is a classical notion), but the expectation values $\langle S_x \rangle$, $\langle S_y \rangle$, and $\langle S_z \rangle$.