# Help understanding easy state problem

narfarnst
First off, I don't need a solution, I just need to make sens of the solution I already have.

## Homework Statement

What state of polarization do the following represent (Give your answer in terms of an angle relative to the transmission axis).
(a). |t> + |a>
(b) |t> + 2|a>
(c) 2|t>-|a>
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My professor has given us the solutions:
(a). arctan(1) = 45 deg.
(b). arctan(2)~65 deg
(c). arctan(-1/2)~27 deg.

From this, I've reverse-engineered that to find the answer in general, for m|t>+n|a> you take arctan(n/m).

But.... what the hell does this mean, and how is it derived?

Thanks.

sgd37
't' stands for transverse and 'a' for axial and all that means is that they are the basis vectors of the polarisation vector and their coefficients are the components. Similar to (x,y) and the angle between them is arctan (y/x)

narfarnst
Thanks.

But why use bra-ket notation? Couldn't you just as easially express them as (a, t). For example, (2, -1) or (1, 1).

sgd37
yes they're equivalent, but the advantages of bra-ket notation are lost in this examble

narfarnst
Ahhh, well thanks again.