Confusion about Dirac Notation (interferometer)

[Edge Of Pain]

Hello everybody,

Dirac notation uses "bras"(<a|) and "kets"(|b>), which are row vectors and column vectors respectively, but what would something like |a, b> mean? It makes no notational sense to me

Context: A couple of photons going through beam splitters in an interferometer. One is in state a and the other is in state b. If we had only 1 photon taking path a, and nothing in path b, then the notation becomes |a, 0>, but I don't know how to reconcile this with Dirac notation.

 

[Orodruin]

which are row vectors and column vectors respectively

This is significantly simplified and only makes sense in a finite dimensional Hilbert space. It is better to think about kets as elements in the state space and bras as elements in the corresponding dual space.

but what would something like |a,b> mean?

States are usually labelled by their quantum numbers. In many cases, one quantum number is not sufficient, such as for eigenstates of the angular momentum squared. Without more information on what a and b are it is difficult to be more specific.