Unformatted text preview: dρ dt = 0 (Liouville s Theorem) . (2) Due February 5 in class (6 points). Read M&T chapter 7.12. (21) Poisson brackets are defned by [ g, h ] = X k ∂g ∂q k ∂h ∂p k∂h ∂q k ∂g ∂p k ! where g and h are ±unctions o± q i , p i and, possibly, t . Show the ±ollowing properties (due February 10 be±ore class, 10 points): 1. dg dt = [ g, H ] + ∂g ∂t . 2. ˙ q j = [ q j , H ] . 3. ˙ p j = [ p j , H ] . 4. [ x i , x j ] = [ p i , p j ] = 0 ; [ x i , p j ] = δ ij , 5. [ x i , L j ] = ² ijk x k , [ p i , L j ] = ² ijk p k , and [ L i , L j ] = ² ijk L k , , where the Einstein summation convention is used and L j = ² jkl x k p l is the i th component o± the angular momentum o± the system....
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 Spring '11
 Berg
 Momentum, Work, Trigraph, Tensor, Covariance and contravariance of vectors, phase space

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