1. The Hamiltonian operator H for a certain physical system is represented bythe matrix100H = hw 020002,while two other observables A and B are represented by the matricesA = 2000 0 21-) --2u 0 0B = 0 0uO0 u 0where à and u are real (non-zero) numbers.If the system is in a state described by the state vectorwhere c, c2 and c3 are complex constants and(i) find the relationship between c1, cz and cz such that uis normalised tounity; and(ii) find the expectation values of H, A and B.(iii) What are the possible values of the energy that can be obtained in ameasurement when the system is described by the state vector u? Foreach possible result find the wave function in the matrix representationimmediately after the measurement.

Given, A=λ010100002 Characteristics matrix for A…

1. The Hamiltonian operator H for a certain physical system is represented by the matrix (1 0 0) H = hw 0 20 002 while two other observables A and B are represented by the matrices A = 1 0 0 0 0 21 (2u 0 0 B-0 04 where à and u are real (non-zero) numbers. If the system is in a state described by the state vector where c, cz and cy are complex constants and (i) find the relationship between c, c2 and c3 such that uis normalised to unity; and (ii) find the expectation values of H, A and B. (iii) What are the possible values of the energy that can be obtained in a measurement when the system is described by the state vectorlu For each possible result find the wave function in the matrix representation immediately after the measurement.

1. The Hamiltonian operator H for a certain physical system is represented by the matrix (1 0 0) H = hw 0 20 002 while two other observables A and B are represented by the matrices A = 1 0 0 0 0 21 (2u 0 0 B-0 04 where à and u are real (non-zero) numbers. If the system is in a state described by the state vector where c, cz and cy are complex constants and (i) find the relationship between c, c2 and c3 such that uis normalised to unity; and (ii) find the expectation values of H, A and B. (iii) What are the possible values of the energy that can be obtained in a measurement when the system is described by the state vectorlu For each possible result find the wave function in the matrix representation immediately after the measurement.