Understanding Spin 1/2 Particles - Writing Expressions

[quantumlooser]

Hello,
I need help understanding spin 1/2 particles and writing down expressions for the amplitidues of spin up/down states as a function of time.
Any help is appreciated or links to other information.
Thanks!

 

[malawi_glenn]

That depends on what hamiltonian etc you have.. if this is a homework question, then post it in the homework forum; the full problem given and your attempt to solution.

 

[denian]

Hello, understanding spin 1/2 particles can be a complex concept, but I will try my best to explain it and provide some resources for you to further your understanding.

Spin 1/2 particles, also known as fermions, are subatomic particles that have a spin of 1/2, which is a fundamental property of these particles. This spin is not a physical rotation, but rather a quantum mechanical property that describes the intrinsic angular momentum of the particle. Spin 1/2 particles are fundamental building blocks of matter, such as electrons, protons, and neutrons.

When it comes to writing down expressions for the amplitudes of spin up/down states as a function of time, we need to first understand the concept of quantum superposition. This is the idea that a particle can exist in multiple states at the same time, with each state having a certain probability of being observed. In the case of spin 1/2 particles, they can exist in two spin states - spin up and spin down, with each having a probability amplitude associated with it.

To write down these expressions, we use the mathematical formalism of quantum mechanics, specifically the Dirac notation. The amplitude for a spin up state is denoted as |u⟩, while the amplitude for a spin down state is denoted as |d⟩. These amplitudes can be written as functions of time, where the probability of observing the particle in a particular spin state is given by the square of the amplitude.

I highly recommend checking out resources such as "Quantum Mechanics" by David J. Griffiths or "Introduction to Quantum Mechanics" by David J. Griffiths and Darrell F. Schroeter for a more in-depth understanding of spin 1/2 particles and quantum mechanics in general. Additionally, online resources such as Khan Academy and MIT OpenCourseWare offer free lectures and tutorials on this topic.

I hope this helps and good luck with your studies!