This preview shows page 1. Sign up to view the full content.
Unformatted text preview: d 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 kh 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 beore 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 ] = ij , 5. [ x i , L j ] = ijk x k , [ p i , L j ] = ijk p k , and [ L i , L j ] = ijk L k , , where the Einstein summation convention is used and L j = jkl x k p l is the i th component o the angular momentum o the system....
View
Full
Document
 Spring '11
 Berg
 Work

Click to edit the document details