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Homework 4

# Homework 4 - Goldstein:9.7,9.25 Inaddition 1 .The x y z px...

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Physics 601 Homework 4---Due Friday October 1 Goldstein: 9.7, 9.25 In addition: 1. This problem uses the result in problem 2 of homework 3 in the context of a 6‐ dimension phase space associated with a single particle in 3 dimensions. The canonical variables are x , y , z , p x , p y , p z . In this problem various transformations with clear physical meanings are proposed. State the physical meaning, show that they are canonical and find the generator of the transformation (as defined in in problem 2 of homework 3) and show it satisfies the relation ξ ( η ; ε ) ∂ε = [ ξ , g ] PB given in problem 2 of homework 3. In all of these ε is a constant. X = x + ε Y = y Z = z P x = p x P y = p y P z = p z a . X = x cos( ε ) + y sin( ε ) Y = x sin( ε ) + y cos( ε ) Z = z P x = p x cos( ε ) + p y sin( ε ) P y = p x sin( ε ) + p y cos( ε ) P z = p z b . X = x Y = y Z = z P x = p x + ε P y = p y P z = p z c . X = (1 + ε ) x Y = (1 + ε ) y Z = (1 + ε ) z P x = (1 + ε ) 1 p x P y = (1 + ε ) 1 p y P z = (1 + ε ) 1 p z d 2. Show that if a one‐parameter family of time‐independent canonical

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Homework 4 - Goldstein:9.7,9.25 Inaddition 1 .The x y z px...

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