If the system is in a state described by the state vector Czu3 where c1, c2 and c3 are complex constants and (i) find the relationship between cı, c2 and c3 such that u is normalised to unity; and
If the system is in a state described by the state vector Czu3 where c1, c2 and c3 are complex constants and (i) find the relationship between cı, c2 and c3 such that u is normalised to unity; and
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Transcribed Image Text:1. The Hamiltonian operator H for a certain physical system is represented by
the matrix
100
H = hw |0 20
00 2
while two other observables A and B are represented by the matrices
- --
(0 λ 0
A = |1 0 0
0 0 22
2μ 0 0'
B =
0 μ 0,
where A and u are real (non-zero) numbers.
If the system is in a state described by the state vector
where c1, c2 and c3 are complex constants and
u
(i) find the relationship between c1, c2 and c3 such that u is 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 vector u? For
each possible result find the wave function in the matrix representation
immediately after the measurement.
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