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consider a physical system with three dimensions. An orthonormal basis from the selected state. On this...

consider a physical system with three dimensions. An orthonormal basis from the selected state. On this basis, Hamiltonian is represented by a matrix :
                         
                          [2 1 0]
                          [1 2 0]
                          [0 0 3]

find the measured system energy value and its basis.When the particles is in state | ψ >,with its basis 1/√3     [    i ]
                        [- i ]
                        [   i ]

Also find <H>,<H^2>,and <∆H>.

                 

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