AW: [Wien] relativistic quantum number

[Gerhard Fecher]

The relativistic angular momentum quantum number is defined as (see textbooks on relativistic quantum mechanics):

kappa = (l-j)(2j+1) 

as there is only one angular momentum quantum number (kappa) needed to distinguish the solutions of the Dirac equation (and not 3 as suggested by l, s, j). kappa can not be zero ! (Note: in some work the sign of kappa may be reversed !)

The multiplicity of each state is (2j+1) as there are (2j+1) states with different projection m_j = -j,...,+j for each j. 

The state with kappa = -1 is the s_(1/2) state with the magnetic quantum numbers m_j=-1/2 and +1/2
The state with kappa = +1 is the p_(1/2) state with the magnetic quantum numbers m_j=-1/2, +1/2
The state with kappa = -2 is the p_(3/2) state with the magnetic quantum numbers m_j=-3/2, -1/2, +1/2, +3/2
and so on ....

You see, there is nothing confusing.

Ciao 
Gerhard

-----Ursprüngliche Nachricht-----
Von: wien-bounces at zeus.theochem.tuwien.ac.at im Auftrag von yxl at email.jlu.edu.cn
Gesendet: Do 15.12.2005 03:24
An: wien at zeus.theochem.tuwien.ac.at
Betreff: [Wien] relativistic quantum number
 
Dear users,
   I'm a biggner,I want to ask a quenstion about relativistic quantum number,how the spin quantum number is defined ? Are +1 and -1 mean spin up and down?In s state there is only one relativistic quantum mumber -1,but in s state occupied numbers is two. I'm in confusion,Please help me! Thanks a lot.
                                              hongxia
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