Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

I have been reading a online-book/blog/material on Quantum Mechanics, when I encountered a notation on a page and I have no idea what it means. See if you can help.

Here's the link and follows the paragraph where I am stuck.

Observe that exchanging either the incoming or the out­going par­ti­cles is tan­ta­mount to exchanging the two alter­na­tives and, cor­re­spond­ingly, the two ampli­tudes, so that A2 takes the place of A1 and vice versa. Since the two ampli­tudes have the same mag­ni­tude, there is a com­plex number c of unit mag­ni­tude such that A2 = A1 c. In other words, mul­ti­pli­ca­tion by c = [1:β] rep­re­sents an exchange of the incoming or out­going particles.

If the incoming or out­going par­ti­cles are exchanged twice, then (i) A1 gets mul­ti­plied by $c^2$ and (ii) the orig­inal sit­u­a­tion is restored. Thus A1 = A1 $c^2$, whence it fol­lows that $c^2$ = [1:2β] = 1. This means that 2β must be equal to an inte­gral mul­tiple of 360°, and this leaves us with two pos­si­bil­i­ties: β = 0°, in which case A2 = A1, or β = 180°, in which case A2 = −A1.

I have put the notation in bold. What is it that the writer means exactly by $[1:\beta] \ \ and \ [1: 2 \beta]$ ?

:)

share|improve this question
add comment

1 Answer 1

up vote 6 down vote accepted

The author uses this weird notation $[c:\gamma]$ to represent complex numbers. It means: c is short for the mag­ni­tude $|c|$ of c, $\gamma$ is the phase of c.

I have never seen this before either ;-).

The author explains it earlier in his book, check out this link.

share|improve this answer
    
The colon is interesting but the square brackets are somewhat standard for polar coordinates and the complex numbers in polar form, see e.g. pages 1 and 66-67 of cimt.plymouth.ac.uk/projects/mepres/alevel/fpure_ch3.pdf –  Luboš Motl Mar 9 '13 at 7:24
2  
I've never seen it before. I've been studying physics and math for 5 years now. –  lomppi Mar 9 '13 at 7:43
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.