Stern Gerlach Spin 3/2, Quantum Mechanics

In summary, the conversation discusses finding the spin 3/2 rotation matrix, with the person stating they have already found the rotation matrices for spin 1/2 and spin 1. They clarify that this is not a homework problem, but rather for studying other spins. The equations for spin 1/2 and spin 1 are provided. The person then asks for help in finding the rotation matrix for spin 3/2, mentioning that it should be a 4x4 matrix. They also mention that they have already worked out the matrices for spin 1/2 and spin 1 and ask for someone to help them with the 4-dimensional representation.
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Homework Statement

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Just trying to find the spin 3/2 rotation matrix, I've found spin 1/2 and spin 1. This isn't a homework problem just studying some other spins.

Homework Equations


For spin 1/2: Rn(Φ) = cos(Φ/2)1ˆ − isin(Φ/2)σn

For spin 1: Un(Φ) = e −iΦSn = 1ˆ − isin(Φ) · Sn − (1ˆ − cos(Φ)) · (Sn) 2

So what is it for spin 3/2? I can't figure out the rotation matrix.

The Attempt at a Solution


Spin 3/2 will be a 4x4 matrix because it has 4 beams (2s+1). However I can't figure it out...

I worked out 1/2 and 1 could someone work out 3/2?
 
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  • #2
You need to provide us with your attempt at doing it in the case of the 4-dimensional representation. Show us what you tried and we may be able to steer you in the right direction.
 

1. What is the Stern Gerlach experiment?

The Stern Gerlach experiment is a landmark experiment in quantum mechanics that demonstrated the existence of particle spin. In this experiment, a beam of silver atoms is passed through an inhomogeneous magnetic field, causing the atoms to split into two distinct beams. This showed that the atoms possess an intrinsic angular momentum or spin, which can have only two orientations.

2. What is spin 3/2 in quantum mechanics?

Spin 3/2 refers to the spin quantum number of a particle in quantum mechanics. This quantum number describes the intrinsic angular momentum of a particle and can have values of either 1/2, 1, 3/2, etc. The spin 3/2 particles, also known as fermions, have four possible spin orientations.

3. How does the Stern Gerlach experiment relate to quantum mechanics?

The Stern Gerlach experiment is a crucial demonstration of the principles of quantum mechanics. It shows that particles have discrete energy levels and can have two distinct orientations of spin. This experiment also proved that the classical laws of physics do not fully apply to the microscopic world and that quantum mechanics is needed to accurately describe the behavior of particles.

4. What is the significance of the Stern Gerlach experiment?

The Stern Gerlach experiment is significant because it provided experimental evidence for the principles of quantum mechanics. It also helped to develop the concept of particle spin, which is now a fundamental aspect of our understanding of subatomic particles. This experiment also paved the way for further research and advancements in the field of quantum mechanics.

5. How does the Stern Gerlach experiment impact our understanding of the universe?

The Stern Gerlach experiment has had a significant impact on our understanding of the universe by showing that the classical laws of physics do not fully apply to the microscopic world. It also helped to develop the theory of quantum mechanics, which has since been applied to various fields such as particle physics, chemistry, and technology. This experiment has revolutionized our understanding of the fundamental building blocks of the universe and continues to be a crucial tool for further research and discoveries.

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