# Help understanding easy state problem

• narfarnst
In summary, the conversation is about finding the state of polarization in terms of angles for various solutions given by a professor. The formula for finding the angle is arctan(n/m), where n and m are the coefficients of the basis vectors 't' and 'a'. The use of bra-ket notation is discussed, with the advantages being lost in this specific example.
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>
-------
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.

'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)

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).

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

Ahhh, well thanks again.

## 1. What is an easy state problem?

An easy state problem is a type of scientific problem that can be solved using simple, well-established techniques and methods. These problems are usually straightforward and do not require advanced technology or extensive research to understand and solve.

## 2. Why is understanding easy state problems important?

Understanding easy state problems is important because it allows scientists to quickly and efficiently solve common problems and make progress in their respective fields. It also helps to build a foundation of knowledge that can be applied to more complex problems in the future.

## 3. How are easy state problems different from difficult problems?

Easy state problems are different from difficult problems in terms of complexity and the level of expertise and resources needed to solve them. While easy state problems can be solved using well-established methods, difficult problems require more advanced techniques and extensive research to find a solution.

Yes, easy state problems can lead to significant scientific advancements. By understanding and solving these problems, scientists can gain valuable insights and make new discoveries that can contribute to the advancement of their field.

## 5. How can scientists identify if a problem is an easy state problem?

Scientists can identify easy state problems by assessing the complexity of the problem, the available resources and methods to solve it, and the level of expertise needed. If the problem can be easily understood and solved using established techniques, it is likely an easy state problem.

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