Problem with making a wavefunction for two particles

1. Mar 9, 2006

mathlete

OK - the question gives me two bosons with 0 spin (and the wavefunctions/energy levels) and tells me to find the total wavefunction and energy for the ground state and first excited state.

Now, I know the total wavefunction must be symmetric. I know the symmetric spatial part. But the spin part, i'm having some problems with. There is only one spin state (since s=0), correct? Now what I do not understand is:

- What is the spin state for s=0?
- Is this spin state symmetric or antisymmetric?
- Does the spin state change going from the ground to the excited state?
- How do I combine it with the spatial part? Just multiply the two together?

Sorry for the many questions but I can't find any of this in my book, it pretty much skips the role of the spin part altogether.

Last edited: Mar 9, 2006
2. Mar 9, 2006

topsquark

Yes, the spin 0 wavefunction is symmetric since it is an even parity state. Spin wavefunctions are simply multiplied onto the spatial wavefunction. (If you were using kets, then the ket space would be a direct product of the waveket and spinket spaces.)

As far as the excited state is concerned, if you are dealing with elementary spin 0 particles, any system you create will also have spin 0, no matter what the energy state is. If your particles are composite (like pions) this need not be true.

-Dan

3. Mar 9, 2006

mathlete

Thanks! That's basically what I thought.

Now I have a problem with the excited states... there should be no triplet, correct (since the bosons both of 0 spin only have one spin state). Why wouldn't it just be the same as the ground state with n=2 plugged in to the wavefunction instead of n=1 (which represents the ground state)?

Last edited: Mar 9, 2006
4. Mar 9, 2006

mathlete

Also, a bit of an unrelated question... what exactly is the difference in notation between the electron configuration (npn'p) and (np, n'p)?

5. Mar 10, 2006

topsquark

That is correct, the triplet and singlet states only occur when combining two spin 1/2 particles.

As I said unless there is some reason for the spin wavefunction to depend on the energy of the particle (and I can't think of a reason why there would be for a spin 0 elementary particle) then the only variation in the overall wavefunction is going to be due to the spatial part.

-Dan

6. Mar 12, 2006

Meir Achuz

Spin just doesn't come in at all.