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QM decomposing linear polarization states

  • Thread starter doublemint
  • Start date
  • #1
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Hello,

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

Given |theta> = (cos[tex]\vartheta[/tex] sin[tex]\vartheta[/tex])
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:

Answers and Replies

  • #2
141
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I believe I found my answer.
Since |theta> = (cos sin), then |pi/2+theta> = (-sin cos)
 
  • #3
fzero
Science Advisor
Homework Helper
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If

[tex] | \theta \rangle = \begin{pmatrix} \cos\theta \\ \sin\theta \end{pmatrix},[/tex]

then it seems natural that

[tex] | \theta + \phi \rangle = \begin{pmatrix} \cos(\theta+\phi) \\ \sin(\theta+\phi) \end{pmatrix}.[/tex]

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.
 
  • #4
8
0
doublemint,

how did u get the one for theta ?

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

thanks in advance
 
  • #5
8
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i think i got it ....... it was right there and i was over complicating things... thank you anyways! :)
 

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