Re: What is a 'doublet', a 'triplet' etc. spin state?

Date: Wed Mar 21 09:26:15 2001
Posted By: Samuel Silverstein, faculty, physics, Stockholm University
Area of science: Physics
ID: 984349953.Ph

Message:

David,

Good question. I could not find many good web references on this topic, although this article on photosynthesis has a decent section ("De-excitation pathways") with nice diagrams of singlet, doublet, and triplet states.

But your question was on why they are called singlet, doublet, and triplet states. This has to do with quantum mechanics. If you measure the spin of a system, you will get two important quantum numbers describing the magnitude and orientation of the spin vector S. The magnitude of S is simply the sum of the spins:

singlet:  1/2 - 1/2 = 0
doublet:  1/2
triplet:  1/2 + 1/2 = 1

Now, the spin of the system can be measured relative to some axis that we define in the lab. Let's call this axis z. Quantum mechanics tells us that the z component of S, or Sz, can only have certain distinct values, separated by integer values of h/2pi.

For a singlet state with zero total spin, both the magnitude and z component of the spin vector is zero, so the only possible eigenstate of S and Sz is:

 
 |0,0>         One eigenstate (singlet)

A doublet state with total spin 1/2 has two possible eigenstates, one with Sz=+1/2 and one with Sz=-1/2:


  |1/2,+1/2>   Two eigenstates (doublet)
  |1/2,-1/2>

Finally, a triplet state with total spin one can have Sz equal 1, 0, or -1:


  |1,1>
  |1,0>        Three eigenstates (triplet)
  |1,-1>

I hope this makes things clearer for you. A more complete (but fairly advanced) description of adding angular momentum can be found at this web site.

Regards,

Sam Silverstein

Current Queue | Current Queue for Physics | Physics archives

Try the links in the MadSci Library for more information on Physics.