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1. Consider the states | w) = 91|) +212) and I x) =-) +2), where the t two vectors are orthonormal. (a) Calculate the operators | v)(x | and | x(v | Are they equal? (b) Find the Hermitian conjugates of w). Iz).I)x l. and I x)Xv

1. Consider the states | w) = 91|) +212) and I x) =-) +2), where the t two vectors are orthonormal. (a) Calculate the operators | v)(x | and | x(v | Are they equal? (b) Find the Hermitian conjugates of w). Iz).I)x l. and I x)Xv

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H.W.2 1. Consider the states | w) = 91 1 1) +212) and | x) = -1o) ++I dal, where the two vectors | d) and I d2) are orthonormal. (a) Calculate the operators | w)(z | and x)(y 1 Are they equal? (b) Find the Hermitian conjugates of w). I z). I w)x I. and xvl 2. Suppose the operators å and B are projection operators. Show that the sum of two projection operators is a projection operator too when their product is zeto.
Transcribed Image Text:H.W.2 1. Consider the states | w) = 91 1 1) +212) and | x) = -1o) ++I dal, where the two vectors | d) and I d2) are orthonormal. (a) Calculate the operators | w)(z | and x)(y 1 Are they equal? (b) Find the Hermitian conjugates of w). I z). I w)x I. and xvl 2. Suppose the operators å and B are projection operators. Show that the sum of two projection operators is a projection operator too when their product is zeto.
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