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

  • Thread starter Thread starter StephenD420
  • Start date Start date
  • Tags Tags
    Bra-ket
Click For Summary

Homework Help Overview

The discussion revolves around quantum states represented by the notation |t> and |a>, specifically in the context of their relationship to angles from the transition axis in polarization. The original poster attempts to understand the implications of the equation |t> + |a> equating to an angle of 45 degrees and seeks clarification on the definitions and meanings of |t> and |a>.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants question the notation and definitions of |t> and |a>, with some suggesting that |t> represents a state transmitted 100% of the time and |a> represents a state absorbed 100% of the time. Others express the need for more information to clarify the problem setup and conventions used in the discussion.

Discussion Status

The discussion is ongoing, with various interpretations being explored. Some participants have offered insights into the nature of the states and their relation to angles, while others are still seeking more information to understand the problem fully.

Contextual Notes

There is mention of a lecture context where |p> is defined in relation to |t> and |a>, and the need for clarity on the conventions used in the class regarding these quantum states. The original poster's understanding of the problem is limited by the definitions of |t> and |a>.

StephenD420
Messages
97
Reaction score
0
|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
 
Physics news on Phys.org
Your notation makes no sense to me, maybe you should write down the problem exactly as it was stated?
 
What states of polarization do the following states represent(specify by an angle from the transmission axis of the polarizer).
a.

|t> + |a>
 
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?
 
That is what I am trying to find out

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

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

Similar threads

Replies
2
Views
2K
  • · Replies 8 ·
Replies
8
Views
3K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
6
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 10 ·
Replies
10
Views
3K