Solving Quick Bra-Ket Question: |t> + |a> = 45°

[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 that's 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.