How Does Time-Dependent Perturbation Impact Electron Spin State Evolution?

[mohammed.omar]

Hello All,

Using Time dependent perterbation we could predict the Rabi precession and the spin states of the electrons, for example, in an external magnetic field. I was wondering how could we calculate the evolution from a random spin state to one of the defined spin states, does it defy the spin quantization during its evolution?

If we could calculate this evolution, could we calculate the minimum length/time required for a Stern-Gerlach apparatus to separate the spin up/down particles?

Also, if we apply the Time-independent perturbation to the study of an electron in a magnetic field, we would reach a state of full spin alignment with the field; this solution is NEVER probable when we apply Time-dependent perturbation. Now should not the time-dependent solution tend to be the time independent solution after a long time?

Regards,

 

[eljose79]

Hi there,

Thank you for your interesting question. The calculation of the evolution from a random spin state to one of the defined spin states can be done using the principles of quantum mechanics. In time-dependent perturbation theory, the evolution of a quantum system is described by a time-dependent Schrödinger equation, which takes into account the external perturbation (in this case, the external magnetic field). The solution to this equation will give us the probability of the electron being in a certain spin state at a given time. This does not defy spin quantization, as the spin states are still quantized and the electron can only be in one of the defined spin states at a given time.

As for calculating the minimum length/time required for a Stern-Gerlach apparatus to separate the spin up/down particles, this can also be done using time-dependent perturbation theory. The time it takes for the particles to separate will depend on the strength of the magnetic field and the initial spin state of the particles.

Regarding your question about the time-dependent solution tending to the time-independent solution after a long time, this is not always the case. In some cases, the time-dependent solution may approach the time-independent solution as time goes on, but this is not a general rule. The time-independent solution represents a stable state, while the time-dependent solution takes into account the perturbation and the resulting changes in the system.

I hope this helps answer your questions. If you have any further inquiries, please don't hesitate to ask.