Spin-1/2 Particle in Superposition B Field: Probability and Interactions

In summary, the conversation discusses the potential scenario of a spin-1/2 particle entering a non-constant B field, with both the particle and the field being in a superposition state. The probability of the B field being up or down would depend on the interaction between the particle and the field, and using silver atoms instead of electrons may provide a clearer understanding of the situation. The possibility of using different state descriptions for spin and the B field is also mentioned. It is suggested to track the evolution of each component individually and combine them afterwards for a better analysis.
  • #1
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Lets say I have a spin-1/2 particle that is about to enter a non-constant B field.
the spin 1/2 particle has a state vector of
[itex] |\psi>= \frac{|+z>}{\sqrt{2}} + \frac{|-z>}{\sqrt{2}}[/itex]
What if the B field was also in a superposition like
[itex] |\psi>= \frac{ \sqrt{2}|+B>}{\sqrt{3}}+\frac{|-B>}{\sqrt{3}} [/itex]
where B is some non constant magnetic field.
How would I figure out what is the probability of the B field being up or down?
Would it also depend on how the electron interacts with it.
Maybe we should change our particle to a neutron so the Lorentz force won't dominate.
 
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  • #2
It is confusing to use the same state description for spin and B-field. I don't know how to get such a superposition, but you can track the evolution of all 4 components (spin up, magnet up, spin up, magnet down, and same for spin down) individually, and add them afterwards.
Instead of electrons, silver atoms can be used.
 

1. What is a spin-1/2 particle in superposition?

A spin-1/2 particle is a type of quantum particle that has an intrinsic angular momentum or spin of 1/2. In superposition, the particle exists in multiple states simultaneously, instead of being in just one state. This is a fundamental property of quantum mechanics.

2. How does a spin-1/2 particle interact with a magnetic field?

A spin-1/2 particle interacts with a magnetic field through its spin. The particle has a magnetic moment, which is influenced by the magnetic field. This interaction results in the particle precessing or spinning around the direction of the magnetic field.

3. What is the probability of finding a spin-1/2 particle in a specific state?

The probability of finding a spin-1/2 particle in a specific state is determined by its quantum state function, which describes the particle's superposition of states. The squared magnitude of the state function gives the probability of finding the particle in a particular state.

4. How does the strength of the magnetic field affect the spin-1/2 particle in superposition?

The strength of the magnetic field affects the spin-1/2 particle in superposition by altering the probability of finding the particle in a specific state. A stronger magnetic field will result in a higher probability of finding the particle in a certain state, while a weaker magnetic field will result in a lower probability.

5. Can a spin-1/2 particle in superposition have an infinite number of possible states?

No, a spin-1/2 particle in superposition can only have a finite number of possible states, which is determined by the number of spin states it can have. For example, an electron, which is a spin-1/2 particle, can have two spin states: spin up and spin down. Therefore, it can have a maximum of two possible states in superposition.

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