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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 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?
Thanks in advance