Problem understanding a statement in Bose Statistics

[Narcol2000]

In a particular book I'm readin on Bose-statistics it metions having a system with two bosons and a large number of energy levels for which the two bosons can occupy. 0, e,2e,3e,4e etc..

It then says the total energy of a quantum state is $$E_{ij} = e_i + e_j$$ and that there is only one quantum state with this energy if i is not equal to j.

This last part makes no sense to me because clearly $$E_{14}$$ and $$E_{23}$$ are separate quantum states with the same energy 5e... unless they mean there is only one state with the energy separated specifically as $$e_1 + e_2$$?

This is bugging me quite a bit so if anyone can confirm whether i on the right track I would be grateful.

 

[Avodyne]

unless they mean there is only one state with the energy separated specifically as $e_1 + e_2$?

Yes, that's what they mean. Are you sure they said that the levels were equally spaced? If not, your problem does not arise.

 

[Narcol2000]

Ah I see makes sense.

The preceeding example in the book was one with equally spaced levels and it wasn't clarified whether the levels in the subsequent example were equally space or not so for consistency i just assumed they were. The book wasn't particularly clear in this respect so I was just a bit confused at the time.

thanks for your reply.