Quick bra-ket question

StephenD420

|t> + |a> = ?? As an angle from the transition axis

now I know it is 45 degrees is the answer but I am not sure what |t> or |a> equals.
I know |theta> = cos theta |t> + sin theta |a>
so how do I go from here?
Does |t> = cos^2 theta
and |a> = sin^2 theta????

Thanks.
Stephen

niklaus

Your notation makes no sense to me, maybe you should write down the problem exactly as it was stated?

StephenD420

What states of polarization do the following states represent(specify by an angle from the transmission axis of the polarizer).
a.

|t> + |a>

niklaus

I still think I would need much more information to answer this question. Do you use some convention in your class what |t> and |a> mean?

StephenD420

That is what I am trying to find out

|t> is the transmission quantum state
|a> is the absorbtion quantum state

The lecture started with
|p> = cos theta |t> + sin theta |a>
and
<t|p> = cos theta
<a|p> = sin theta

StephenD420

bump...

would |t> be cos theta
and |a> sin theta

what would these represent where
|t> + |a> is 45 degrees
|t> + 2|a> is 63 degrees
2|t> - |a> is 27 degrees

please help me figure out what |t> and |a> represent!!!

Thanks.

squigglywolf

uhh just guessing but by looking at that notation, |p> = |t> should represent a state that will be transmitted 100% of the time, and |p> = |a> represents a state that will be absorbed 100% of the time. So a state |p> =1/sqrt(2)[ |t> + |a> ] should represent a state thats in a superposition of these two states, and so there is a 50/50 chance of it being absorbed or transmitted when it encounters the polarizing filter. So quantum mechanically the state of the system is either |t> or |a> when it interacts with the polarizer and that decides whether or not it is transmitted. I guess this would translate classically to a polarizer whose angle is at 45degrees, since as you said, |p> = cos theta |t> + sin theta |a>. The polarizing angle just determines how much of each of the states |a> and |t> you have at any given time. They are orthogonal states.