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A single spin ½ quantum particle is prepared in a linear combination of its two spin-z...

A single spin ½ quantum particle is prepared in a linear combination of its two spin-z eigenstates. At time t = 0, the state is ∣ ψ >= 4 5 ∣↑ > z + 3 5 ∣↓ > z and placed in a uniform magnetic field that is directed along the z-axis.

Which of the following vary with time for t > 0?  

I. < S z >

II. < H > (Hamiltonian)

III. P ↑ z (Probability the particle will be found in ∣ ↑ > z)

IV. P ↑ y (Probability the particle will be found in ∣ ↑ > y )

Solutions

Expert Solution

Option IV is correct. The probability of finding the particle in up state of y direction is time dependent. The reson is elaborated in the following pictures:

genius_generous answered 2 years ago
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