Review Problems for Test 2

QUESTION

Review Problems for Test 21. Which of the following are Hermitian operators?(a) XPy(b) XPx(c) HX(d) XPx X2. Evaluate the expectation value of Lx and L2 in the statey1 + 2i|ψ = √ |2 − 111z2+ √ |1011z3. An angular momentum system with l = 1 is prepared in the state1|ψ = √ |1114z3− √ |1014z2+ i √ |1 − 114z(a) What are the possible result of a measurement of the angular momentum component Lz ,and with what probabilities will they occur?(b) Suppose that the Lz measurement leads the result − .. Subsequent to that result, asecond measurement is performed to measure the angular component Lx . What are thepossible results of the measurement, and with what probabilities will they occur?4. Consider a two dimensional ket space. In the basis of two orthonormal kets |1 and |2 , theoperators A and B are represented by_A=1 00 3B=01−i1+i0(a) Do the operators A and B commute?(b) Find the eigenvalues and normalized eigenvectors of both operators1

ANSWER:

REQUEST HELP FROM A TUTOR