1/2 spin particle in a norm-constant magnetic field

[christianpoved]

Hello everybody, I have a curious exercise, there is a 1/2 spin particle in a magnetic field $\vec{B}(t)$ with $||\vec{B}(t)||$ constant, orientated in an angle $\theta$ from the $z$ axis rotating with an angular speed $\Omega$. The hamiltonian will be

$$H(t)=-\vec{S}\cdot\vec{B}$$

How do I solve the Schrödinger equation for this problem?

 

[Ravi Mohan]

Hello everybody, I have a curious exercise, there is a 1/2 spin particle in a magnetic field $\vec{B}(t)$ with $|\vec{B}(t)|$ constant, orientated in an angle $\theta$
from the $z$ axis rotating with an angular speed $\Omega$. The hamiltonian will be

$H(t)=-\vec{S}\cdot\vec{B}$

How do I solve the Schrödinger equation for this problem?

It is nicely done in Quantum Computation and Quantum Information (Neilsen and Chuang) section 7.7.2.

 

[christianpoved]

Whoa... thanks, but I feel that i don't understand the solution (i haven't taken the QM course yet), why are they using the pauli matrices in the hamiltonian?

 

[Ravi Mohan]

Well because the spin operator for spin-half particles is written in terms of Pauli's matrices. When we take the 'dot product' of magnetic moment (which is spin operator multiplied by some factor) with magnetic field, we get Hamiltonian as some combination of Pauli's matrices.

May I suggest to revisit this problem after you have completed quantum mechanics course? :)

 

[christianpoved]

Hahahahahaha, I will check it again after i take QM but I have to do it for some "Geometry for physicists" course that I'm taking, is sad that the math is clear but not the physics :(