Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
Consider the states | w) = 9i 1) +21 2) and | x) = -1 41) +12), where the two vectors | ø1) and 2) are orthonormal. (a) Calculate the operators | w)(x | and | x)(w l. Are they equal?

Consider the states | w) = 9i 1) +21 2) and | x) = -1 41) +12), where the two vectors | ø1) and 2) are orthonormal. (a) Calculate the operators | w)(x | and | x)(w l. Are they equal?

icon
Related questions
Question

1. Consider the states | w) = 9i | ø1) + 2 | $2) and | x) = - I ø1) +I 02), where the two vectors l ø1) and | ø2) are orthonormal. (a) Calculate the operators | w)(x | and | x)(w |. Are they equal? (b) Find the Hermitian conjugates of w), I x), I w)(x 1, and | x)(w I. 2. Suppose the operators  and B are projection operators. Show that the sum of two projection operators is a projection operator too when their product is zero.
Transcribed Image Text:1. Consider the states | w) = 9i | ø1) + 2 | $2) and | x) = - I ø1) +I 02), where the two vectors l ø1) and | ø2) are orthonormal. (a) Calculate the operators | w)(x | and | x)(w |. Are they equal? (b) Find the Hermitian conjugates of w), I x), I w)(x 1, and | x)(w I. 2. Suppose the operators  and B are projection operators. Show that the sum of two projection operators is a projection operator too when their product is zero.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer