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Yeah, I did. I was also getting mixed up over how to take the direct sum of two vector spaces. But now I see how it all works. Cheers!

Hi, I'm trying to understand the fiber bundle formulation of gauge theory at the moment, and I'm stuck on the connection. Every reference I've found introduces the idea of a connection on a principle bundle as a kind of partitioning of the tangent space at all points in the total space into a...

Homework Statement Say I have a set of consecutive integers up to N, for example up to 5, the set 1,2,3,4,5. I need to know a general formula for the value of the sum of all products that can be formed from a certain number of elements taken from such a set. For example with the 5 set, say I...

Okay. This time I really do understand. You're a lifesaver, cheers!

Thanks for replying. That seems perfectly reasonable, but basically my supervisor wants it done in this manner so there's not much I can do ;-) I'll be going up a couple more excitation levels, maybe only one, but obviously we're in computer territory even with a 9x9 matrix, and the project is...

Hi again, everything worked out nicely with the first excitation subspace, got good results, but now I'm stuck thinking about the second! The second subspace hamiltonian looks like [0 1 0] [1 0 1] [0 1 0]albeit multiplied by root two, but that's irrelevant. How can I associate my base states...

Ah, okay. That makes sense. Thanks a bunch, everyone.

Just to make it clearer, say I chose my initial state to be |psi(0)>= |1>a|0>b, and call the eigenvectors \left(\begin{array}{cc}1\\1\end{array}\right) = |A>and\left(\begin{array}{cc}-1\\1\end{array}\right)= |B> I would then want to find coefficients such that |psi(0)> = a1|A> + a2 |B> To...

I'll explain the problem fully. I was trying to avoid it because it's rather long but I guess I should've just done it straight away. We consider two magnetically coupled quantum harmonic oscillators. Call them A and B. Our goal is to extract the dynamics of excitation exchange; for example...

I see. I'll try doing that then. Thanks.

Sorry if I was unclear. |a> is not the state of the whole system, it is one of the eigenvectors of the Hamiltonian. Actually, for my purposes, it is an eigenvector of an excitation subspace of the interaction part of the total Hamiltonian. My example |a> was meant to be...

Homework Statement Hi. This isn't really a 'problem' as such but it is to do with coursework and seems a little too basic to be posted in the maths section. I need to know the result of an arbitrary bra, <an|, say, representing an eigenvector of a system, acting on a compound ket such as...