Does a Spin (1/2) Particle's Hamiltonian State Imply Its Spin Orientation?

[Void123]

Homework Statement

If I am told a spin (1/2) particle is originally in the state of a particular Hamiltonian (proportional to S(z)), does that imply the general state or spin-up? Because I am asked to find the probability that it will change its spin, which I can only make sense of assuming its talking about a specific spinor (in this case up).

Homework Equations

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The Attempt at a Solution

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[Void123]

I received an email saying someone replied to this thread. Was the post deleted?

 

[berkeman]

I received an email saying someone replied to this thread. Was the post deleted?

Yes, the poster deleted his own post. Possibly because he realized that he did too much work on solving this schoolwork question. Perhaps he will come back and post more of a hint or a leading question...

 

[Void123]

Straightened it out. Am I supposed to get an energy transition value of h-bar, from spin-up to spin-down state? I imagine so since the eigenvalue of angular momentum is increased/decreased by h-bar. Right?

 

[paranormal]

It seems that there may be some confusion about the terminology being used. When we say a spin (1/2) particle is in a particular Hamiltonian, we are referring to the system's energy and how it changes over time. This does not necessarily imply a specific spin state, such as spin-up. To find the probability of a spin change, we would need to know the initial spin state and the specific Hamiltonian being used. It is possible that the problem is asking for the probability of a spin change in a general state, rather than a specific spin state. It would be helpful to clarify the wording of the problem to ensure a correct solution.