1. Let |+) and |-) be an orthonormal basis in a two-state system. A new set of kets 01) and 2) are defined as 1 √2 1 |02

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1 Let And Be An Orthonormal Basis In A Two State System A New Set Of Kets 01 And 2 Are Defined As 1 2 1 02 1 (62.25 KiB) Viewed 72 times

1. Let |+) and |-) be an orthonormal basis in a two-state system. A new set of kets 01) and 2) are defined as 1 √2 1 |02) √2 (a) Show that 01) and 2) is an orthonormal set. (b) Express |+) and |-) in terms of |01) and 2). |01) = - (+)- e|-)) (e-i|+)+|-)) (c) Let the operator A be defined as A = |+)(-+ |-)(+1. Is A hermitian? What is the matrix representation of A in the basis {+), |-)}? (d) Express A in terms of the bras and kets of . Find the matrix representation of A in the new basis {01), 2)}. (e) For which value of 0 is the matrix representation of A diagonal?