Magnetic field and spin

In summary, the question involves calculating the minimum time for a beam of neutrons with initial spin up along the z direction to exit a uniform 1 tesla magnetic field in the y direction with their spins along -z. This can be done using the time-dependent Hamiltonian and the time evolution operator, with the magnetic moment of the neutron being -0.966x10^-26 J/T. The energy required to flip each neutron can be calculated using the equation H = u . B, and the Heisenberg picture can be used for solving this problem. A book on advanced quantum mechanics can provide further assistance with this fundamental calculation.
  • #1
v_pino
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Homework Statement



A beam of neutrons traveling in the x direction initially has all its spins up along the z direction. The neutrons pass through a region in which there is a uniform 1 tesla magnetic field in the y direction. What is the minimum time t the neutrons need to remain in the field to exit it with their spins along -z? The magnetic moment of the neutron is u=-0.966x10^-26 J/T.

Homework Equations



Is this question to do with time-dependent Hamiltonian? If so, does this equation help?

[tex] B=B_0+B_1=B_0 \hat z + b_1(\hat x cos \omega t - \hat y sin \omega t) [/tex]


The Attempt at a Solution



Please help me get started. Thank you.
 
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  • #2
the energy required to flip each neutron is H = u . B, where the terms on the right are vectors. in a time varying field B, and using the Heisenberg picture in which the states are constants of time (which is very useful for solving this problem) one can define the time evolution operator such that the generator is the hamiltonian for the system. there's quite a lot involved in answering this question which I may or may not be able to help you with. ultimately the time evolution operator gives you the new states when operating on the old states, and there you can see the coefficients which give you the equation for resonance times of the required flipping.
almost any book on advanced quantum mechanics will help you with this, as its one of the most fundamental calculations
 

1. What is a magnetic field?

A magnetic field is a region in space where a magnetic force can be detected. It is created by moving electric charges and can interact with other magnetic fields and magnetic materials.

2. How is a magnetic field created?

A magnetic field is created by moving electric charges, such as the movement of electrons in an electric current. It can also be created by certain types of magnets or by the Earth's core.

3. What is spin in relation to magnetic fields?

Spin is an intrinsic property of particles, such as electrons, that causes them to behave like tiny magnets. This spin is responsible for the magnetic properties of materials and the interactions between magnetic fields.

4. How does spin affect the behavior of particles in a magnetic field?

The spin of a particle determines its orientation and direction of rotation. In a magnetic field, particles with spin will align themselves with the direction of the field, causing them to either be attracted or repelled by other magnetic materials.

5. Can spin be manipulated or controlled?

Yes, spin can be manipulated through various methods such as applying an external magnetic field, changing the temperature, or using specialized materials. This is an important aspect in technologies such as MRI machines and computer hard drives.

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