Stern Gerlach Spin 3/2, Quantum Mechanics

[Tphysics]

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?

 

[Orodruin]

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.