Extra-problems-ch3.pdf x HW5.pdf x + Birzeit University [PS] |❘ https://ritaj.birzeit.edu/bzu msgs/attach/887815/Extra problems ch3.pdf Extra-problems-ch3.pdf Type here to search 2/2 5. Consider a three-level system where the Hamiltonian and observable A are given by the matrix. 0 10 A-101 0 10 100 Ĥ= hw 01 0 001 (a) What are the possible values obtained in a measurement of A (b) Does a state exist in which both the results of a measurement of energy E and observable A can be predicted with certainty? Why or why not? (e) Two measurements of A are carried out, separated in time by t. If the result of the first measurement is its largest possible value, determine the expectation value <(t)|A)t) > for the second measurement. 6. Consider a two level system, where the matrix representation of the position operator and its eigenvectors are given by: x = -(8%) |1 1>= (6) 12 2>= (°) and that the Hamiltonian of the system is given by: Ĥ = -( Ee-e - Eo (a) Is the Hamiltonian operator hermitian? Justify your answer! (b) Is it possible to find common eigenstates for Ĥ and ? Justify! (e) Are states 1 and 2 > stationary? (d) Find eigenvalues and eigenvectors of the Hamiltonian (e) If the electron initially at state |2> write its wavefunction at any later time t (f) Is the operator & constant of motion? Justify your answer Activate Windows Go to Sellings to activate Window ENG 10:33 PM 12/8/2018 m