Spin interaction with B field

In summary, the conversation discusses a problem on page 10 of a document and the corresponding equations and attempted solution. The problem involves finding the probability of a column vector using spinors and taking into account a magnetic field in the z direction. The person expresses confusion about the use of matrices in the problem.
  • #1
forceface
9
0

Homework Statement


The problem is stated on page 10 and it is number 9. http://panda.unm.edu/pandaweb/graduate/prelims/QM_F11.pdf

Homework Equations


I know how to write Sy in the z basis for either spin up or down and I have all the spinors.

The Attempt at a Solution


I tried solving for |ψ(t)> by using Bo as the hamiltonian but that seems to give me an answer that a is single solution and I was expecting a column vector as a solution. If I got a column vector I would just take the inner product of |<Sy|ψ(t)>|2 and that would give me the probability. With this said I feel like I am approaching this problem wrong and I have to take into account that fact that the magnetic field is in the z direction.
 
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  • #2
Hmm what you say above doesn't make much sense to me because [itex]S_y[/itex] and [itex]H[/itex] are supposed to be matrices.

:confused:
 

What is spin interaction with B field?

Spin interaction with B field refers to the phenomenon in which the spin of a charged particle, such as an electron, is affected by a magnetic field. This interaction is a fundamental principle in quantum mechanics and is essential for understanding the behavior of particles at the atomic and subatomic level.

How does spin interaction with B field occur?

Spin interaction with B field occurs when the magnetic moment of a particle, which is created by its spin, interacts with an external magnetic field. This interaction causes the particle to experience a torque, which can result in changes in its orientation and energy state.

What is the significance of spin interaction with B field?

The significance of spin interaction with B field lies in its role in determining the energy levels and behavior of particles in the presence of a magnetic field. This principle is crucial for understanding the properties of atoms, molecules, and materials, and has important applications in areas such as nuclear magnetic resonance and magnetic data storage.

How is spin interaction with B field related to spin quantum number?

The spin quantum number, denoted as s, is a fundamental property of particles that describes their spin and the strength of their interaction with a magnetic field. The value of s determines the number of possible spin states a particle can have, with s=1/2 being the most common value for electrons.

What factors affect the strength of spin interaction with B field?

The strength of spin interaction with B field depends on several factors, including the strength and direction of the external magnetic field, the spin quantum number of the particle, and the properties of the magnetic moment of the particle. Additionally, the type of material and its atomic structure can also affect the strength of this interaction.

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