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Unformatted text preview: PHYS 507 Homework II (Fall ’05) Assigned: October 10, 2005, Monday. Due: October 19, 2005, Wednesday, at 5:00 pm. 1. Consider a three dimensional Hilbert space. Let { 1 i ,  2 i ,  3 i} be an orthonormal basis for this space. Let  ψ i and  φ i be two particular kets with the following expansions  ψ i = 1 √ 2 (  1 i +  2 i ) ,  φ i = 1 √ 3 (  2 i + (1 + i )  3 i ) . Let A be an operator defined as A = 2  ψ ih ψ  + 6  φ ih φ  . In this problem, we will find the matrix representations of these objects in the basis { 1 i ,  2 i ,  3 i} . (a) What are the matrix representations of  ψ i and  φ i ? (b) What are the matrix representations of h ψ  and h φ  ? (c) What are the matrix representations of  ψ ih ψ  and  φ ih φ  ? (d) What is the matrix representation of A ? (e) What are the matrix elements A 23 and A 32 ? (f) What is A  3 i and what is its matrix representation?...
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This note was uploaded on 02/11/2012 for the course MATH 435 taught by Professor Starg during the Spring '11 term at Al Ahliyya Amman University.
 Spring '11
 starg

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