# QM decomposing linear polarization states

doublemint
Hello,

I am trying to decompose |(pi/2)+$$\vartheta$$> into canonical basis. I have done it for |$$\vartheta$$> but i am unsure about what to do with the pi/2.

Given |theta> = (cos$$\vartheta$$ sin$$\vartheta$$)
I was thinking that pi/2 becomes (0 i) and I would add the two vectors together.

Any help would be appreciated!
Thank You
DoubleMint

Last edited:

doublemint
I believe I found my answer.
Since |theta> = (cos sin), then |pi/2+theta> = (-sin cos)

Homework Helper
Gold Member
If

$$| \theta \rangle = \begin{pmatrix} \cos\theta \\ \sin\theta \end{pmatrix},$$

then it seems natural that

$$| \theta + \phi \rangle = \begin{pmatrix} \cos(\theta+\phi) \\ \sin(\theta+\phi) \end{pmatrix}.$$

Also, note that adding quantum states means something completely different from writing down a state whose parameters are the sum of two numbers. The first is a superposition of two states, each with definite quantum numbers.

turab16
doublemint,

how did u get the one for theta ?

I am going over his class examples and can't seem to get it..