A pair of spin-1/2 particles are subject to the Hamiltonian, Ĥ = a(Ŝ₁ + bŜ₂) · (Ŝ₁ + bŜ₂), where Ŝ₁ is the spin operator for the first particle, Ŝ₂ is the spin operator for the second particle, and a and b are positve constants. At time t = 0, the spins are prepared in the state in which the spin of the first particle points in the positive x direction and the spin of the second particle points in the positive y direction. What is the probability the spins are observed at time t > 0 in a state where both spins point in the positive z direction?
A pair of spin-1/2 particles are subject to the Hamiltonian, Ĥ = a(Ŝ₁ + bŜ₂) · (Ŝ₁ + bŜ₂), where Ŝ₁ is the spin operator for the first particle, Ŝ₂ is the spin operator for the second particle, and a and b are positve constants. At time t = 0, the spins are prepared in the state in which the spin of the first particle points in the positive x direction and the spin of the second particle points in the positive y direction. What is the probability the spins are observed at time t > 0 in a state where both spins point in the positive z direction?
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Transcribed Image Text:3. A pair of spin-1/2 particles are subject to the Hamiltonian,
Ĥ ` = a(Ŝ₁ + bŜ₂) · (Ŝ₁ + bŜ₂),
where Ŝ₁ is the spin operator for the first particle, Ŝ₂ is the spin operator for the second
particle, and a and b are positve constants. At time t = 0, the spins are prepared in the
state in which the spin of the first particle points in the positive x direction and the spin
of the second particle points in the positive y direction. What is the probability the spins
are observed at time t > 0 in a state where both spins point in the positive z direction?
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