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21 lines
571 B
Plaintext
21 lines
571 B
Plaintext
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Precession of a Spin-1/2 Particle in a Constant Magnetic Field
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Find Hamiltoninan (pic)
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Find eigenstates of the Hamiltonian (pic)
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Find time-progression expression
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Û(t) = exp(-ι Ĥ t/ħ) = exp(-ι ωₒt S𝓏/ħ) = exp(-ι θ S𝓏/ħ)
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Û(t) = R̂(σk̂)
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⸜ ⸝
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Rotational Operator
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So for arbitrary t (pic)
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Projection along 𝓏-axis? <+𝓏|Ψ(t)>
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--->Why for (-x)-axis does this turn out to be sin²(ω₀ t/2)
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Hw->Find projection of 𝓎-axis
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