How Do Spin Components of a Neutral Particle Vary in a Uniform Magnetic Field?

[Fips]

Homework Statement

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

Homework Equations

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

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 Schrödinger'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?

Thanks in advance

 

[DrClaude]

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 $\langle S_z \rangle$.