Poisson Brackets Explained: Understanding the Relationship between {x,p} = 1"

[gijoe]

can anyone tell me why the poisson brackets for {x,p} = 1 ..from (dx/dx)(dp/dp) - (dx/dp)(dp/dx)... shouldn this equal 0??

 

[Phlogistonian]

I don't know why you think it should be 0.

Calculate each derivative and plug the values into the formula. You should get 1. Remember that x and p are independent.

 

[nicksauce]

dx/dx = 1. dp/dp = 1. dx/dp = 0. dp/dx = 0. 1 - 0 = 1. Which of these is not clear to you?

 

[gijoe]

oh right, my lecture notes said that (dx/dp) = 1... i then assumed that (dp/dx) = 1.. oh yes and p is velocity dependent, now i get it... thanks!

 

[quantumfireball]

{x,p} = 1 therefore
(dx/dx)(dp/dp) - (dx/dp)(dp/dx)=i