A three-level system is prepared in the state: 1) = (1) + c2/2) + c3|3), where (1), (2) and (3) are orthonormal kets, an

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A Three Level System Is Prepared In The State 1 1 C2 2 C3 3 Where 1 2 And 3 Are Orthonormal Kets An 1 (47.7 KiB) Viewed 59 times

A three-level system is prepared in the state: 1) = (1) + c2/2) + c3|3), where (1), (2) and (3) are orthonormal kets, and c; G = 1, 2, 3) are complex constants. A measurement apparatus can distinguish whether or not the system is in the state la) (11) + 2) + 3)) //3. Specifically, its reading is 1 if the system state is (a) and its reading is zero if the system state is orthogonal to la). (a) If the system is measured by the apparatus, what is the probability of getting the reading value 1? (b) The quantity that the apparatus measures correspond to an observable as an operator in quantum mechanics. Find the matrix form of this operator using (1), (2) and (3) as basis. (C) For the observable in (b), find its expectation value and variance for the given quantum state above. (d) The system is measured by the apparatus and it is found that the reading is zero. Based on this measurement outcome, what is the state of the system after the measurement?