Summary: please help me understand the following questions from Physics GRE test Thank you very much! To be honest i really hate this formalism. Memorizing such things is pain. but like everything it is what it is
Why does the derivation of the Dirac equation naturally lead to spin ½ particles? The equation is derived from very general starting assumptions, so which of these assumptions has to be wrong to give us a spin-0 or spin-1 particle?
I have tried to search for an answer and got as far as this...
I am studying the deuterium's nucleus.
As we know, there are just two eigenstates for a spin 1/2 particle: either spin up or spin down.
Thus, over the whole nucleus, you get 4 possible combinations:
1) Spin up-spin up
2) Spin up-spin down
3) Spin down-spin up
4) Spin down-spin down
If you...
1. Homework Statement
Given the expression
s_{\pm}|s,m> = \hbar \sqrt{s(s+1)-m(m\pm 1)}|s,m \pm 1>
obtain the matrix representations of s+/- for spin 1/2 in the usual basis of eigenstates of sz
2. Homework Equations
s_{\pm}|s,m> = \hbar \sqrt{s(s+1)-m(m\pm 1)}|s,m \pm 1>
S_{+} = \hbar...
In the paper "Steady-state spin synchronization through the collective motion of trapped ions" it states the following:
"Steady-state synchronization of atomic dipoles forms the foundation for ultra-stable optical lasers utilizing
narrow-linewidth atoms coupled to a lossy cavity mode. The...
1. Homework Statement
The ground state energy of 5 identical spin 1/2 particles which are subject to a one dimensional simple harkonic oscillator potential of frequency ω is
(A) (15/2) ħω
(B) (13/2) ħω
(C) (1/2) ħω
(D) 5ħω
2. Homework Equations
Energy of a simple harmonic oscillator potential...