Problem with making a wavefunction for two particles

[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.

 

[topsquark]

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.

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

 

[mathlete]

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

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 into the wavefunction instead of n=1 (which represents the ground state)?

 

[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)?

 

[topsquark]

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 into the wavefunction instead of n=1 (which represents the ground state)?

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

 

[Meir Achuz]

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.

Spin just doesn't come in at all.