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Unformatted text preview: PHYS851 Quantum Mechanics I, Fall 2009 HOMEWORK ASSIGNMENT 10 Topics Covered: Tensor product spaces, change of coordinate system, general theory of angular mo- mentum Some Key Concepts: Angular momentum: commutation relations, raising and lowering operators, eigenstates and eigenvalues. 1. [10 pts] Consider the position eigenstate | vector r ) . In spherical coordinates, this state is written as | r ) , where vector R | r ) = rvectore r ( , ) | r ) . In cartesian coordinates, the same state is written | xyz ) , where vector R | xyz ) = ( xvectore x + yvector e y + zvectore z ) | xyz ) . Evaluate the following: (a) ( r | r ) (b) ( r | xyz ) (c) ( r | p x p y p z ) (d) ( r | vector R | r ) (e) ( r | Z | r ) (f) ( r | P z | r ) 2. [10 pts] Consider a system consisting of two spin-less particles with masses m 1 and m 2 , and charges q 1 and q 2 ....
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