Solutions to Quantum Mechanics Homework Set 8 (Problems 1 and 2), Assignments of Quantum Mechanics

Download Solutions to Quantum Mechanics Homework Set 8 (Problems 1 and 2) and more Assignments Quantum Mechanics in PDF only on Docsity! PHY 389K Quantum Mechanics, Homework Set 8 Solutions Matthias Ihl 04/14/2008 Note: I will post updated versions of the homework solutions on my home- page: http://zippy.ph.utexas.edu/~msihl/teaching.html 1 Problem 1 The total angular momentum of the initial state is ~J = ~S = 1. In order to conserve total angular momentum, the final state should have ~J = ~L = 1. The parity of the initial state is even, whereas the parity of the final state is (+)(+)(−)L. For L = 1, parity is not conserved. Therefore, it is impossible to conserve total angular momentum and parity simultaneaously, thus the reaction is forbidden. 2 Problem 2 Let us write the transformation (R, s,~v,~a) (~r, t) in terms of matrices: ( R ~v 0 1 ) ( ~r t ) + ( ~a s ) . (1) Then, (R′, s′, ~v′,~a′) (R, s,~v,~a) (~r, t) can be written as ( R′ ~v′ 0 1 ) [( R ~v 0 1 )( ~r t ) + ( ~a s )] + ( ~a′ s′ ) = ( R′R R′~v + ~v′ 0 1 ) ( ~r t ) + ( R′~a + ~v′s + ~a′ t + s + s′ ) , 1