Consider a self-adjoint operator A. The wavefunction of the system is psi. Use t
ID: 989107 • Letter: C
Question
Consider a self-adjoint operator A. The wavefunction of the system is psi. Use the rules for calculating with scalar products to show that the expectation value (A) = psi/A psi) is real. Do not assume that psi is an eigenfunction of A. Mark with a cross [X] where any of the following statements is wrong. Mark the field like this f. where the statement is correct. If there exists a Heisenberg uncertainty for a pair of observable quantities (observables) A and B it means that neither A nor B can be measured precisely If there exists a Heisenberg uncertainty for a given pair of observables A and B. it means that they cannot have well defined values simultaneously Let the commutators [A. B] = 0 and [A. C) O. This means that a Heisenberg uncertainty exists between A and B. but not between A and C. Let the commutator [A, B) = O. This means that eigenfunctions of A are also eigenfunctions of B and vice versa. The eigenvalues of any operator A are real. For the cases which you identified wrong statement, provide the reason why it is wrong along with a correct version of the statement.Explanation / Answer
3.Operators
1 False
According to the uncertainty principle it is not possible to measure precisely and SIMULTANEOUSLY both the properties. This implies that one property can be measured precisely but there will be an uncertainty in the other property.. Hence the statement that neither A nor B can be measured precisely is wrong
2Correct
3 False
The operators of the properties A and B commute whereas the operators of the properties A and C do not commute.
The Heisenberg’s uncertainty exists between properties whose operators do not commute. So Heisenberg’s uncertainty exist between A and C and not between A and B
4 Correct
5 The eigenvalues of the operators of observable properties are real because the observable properties are real
Please post the remaining questions as new questions