Re: So^' sie^u phu+'c

[Dam Son <son@fermi.phys.washington.edu>]

On Tue, 11 Mar 1997, Hong Lam Vu wrote:

> Hi folks,
> 
> Hu? le^'u tui di ho.c thi` do^'t nha^'t lo+'p ve6` toa'n, thi DH thi`
> suy't ro+'t ddi ta^y chi? vi` ddie^?m toa'n, dda~ kho^ng bie^'t gi` ve^`
> to'an la.i cu+' thi'ch no'i chuye^.n so^' ma'. Nha^n ba'c Paul raise vu.
> so^' a^m so^' duo=ng le^n, tui intuitively nho+' co' la^`n ddo.c dda6u
> ddo' ve^` so^' sie^u phu+'c cu?a o^ng Hamilton co' da.ng a + bi + cj + dk,
> trong ddo' i^2=j^2=k^2= -1,
> ij=-ji, ik=-ki, jk=-kj.
>
> Ca'c ba'c hu? toa'n (ba'c Zu~ng, etc.) va` hu? ly' (ba'c So+n, ba'c
> Tie^'n, etc.) la`m o+n cho bie^'t u+'ng du.ng cu?a so^' sie^u phu+'c
> na`y vo+'i, ma` so^' sie^u phu+'c na`y ta ne^n hie^?u la` the^' na`o ho+?
> ca'c ba'c?? Nghe no'i co' lie^n quan dde^'n spin.

Hi,

Vo+'i bo.n hu? ly' thi` quaternion ddo+n gia?n nhu+ Maria. Bo.n na`y
kho^ng ddu`ng quaternion ma` du`ng ma tra^.n Pauli, la` ca'c ma tra^.n
2x2, ddi.nh nghi~a nhu+ sau: 

             0  1               0  -I               1   0
     s_1 = (      ),    s_2 = (       ),    s_3 = (       )
             1  0               I   0               0  -1


O+? dda^y I la` ddo+n vi. a?o, I^2=-1.  Ca'c so^' quarternion lie^n he^. 
vo+'i ma tra^.n Pauli nhu+ sau: i=-I*s_1, j=-I*s_2, k=-I*s_3. Ca'c ba'c
cu+' du`ng phe'p nha^n ma tra^.n bi`nh thu+o+`ng nha^n ra la` kha('c
nha^.n ddu+o+.c i^2=j^2=k^2=ijk=-1 va` ca'c he^. thu+'c kha'c.

Trong co+ ho.c lu+o+.ng tu+?, hi`nh chie^'u cu?a spin cu?a electron le^n 3
tru.c toa. ddo^. la` hbar*s_1/2, hbar*s_2/2, hbar*s_3/2, hbar la` ha(`ng
so^' Planck: hbar=1.05e-34 Joule*sec (trong co+ ho.c lu+o+.ng tu+? ca'c
dda.i lu+o+.ng va^.t ly' kho^ng pha?i la` so^' ma` dda.i kha'i la` ma
tra^.n). 

Ve^` mo'n o^'c...o^'c gi` ddo' ba'c Aiviet no'i to+'i thi` to^i mu` ti.t. 

So+n.