hw2 - PHYS 507 Homework II (Fall ’05) Assigned: October...

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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.

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hw2 - PHYS 507 Homework II (Fall ’05) Assigned: October...

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