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.