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

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The discussion clarifies why the Poisson bracket {x, p} equals 1, emphasizing the calculation of derivatives. Participants explain that dx/dx and dp/dp both equal 1, while dx/dp and dp/dx equal 0, leading to the result of 1. A misunderstanding regarding the derivatives is addressed, particularly the assumption that (dx/dp) and (dp/dx) could both equal 1. The relationship between position (x) and momentum (p) is highlighted, with p being velocity-dependent. The conclusion reinforces the correct interpretation of the Poisson bracket as {x, p} = 1.
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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??
 
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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.
 
dx/dx = 1. dp/dp = 1. dx/dp = 0. dp/dx = 0. 1 - 0 = 1. Which of these is not clear to you?
 
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!
 
{x,p} = 1 therefore
(dx/dx)(dp/dp) - (dx/dp)(dp/dx)=i
 
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