QM Lecture 10 Part 2

CHAPTER-10 WAVEFUNCTIONS, OBSERVABLES and OPERATORS 

Part 2

10.5 Properties of Operators

        10.5.A  Hermitian conjugate ( or adjoint ) operators  

        10.5.B  Hermitian or self-adjoint operators  

                      Properties of Hermitian (or self-adjoint) operators:

                   -  Operators associated to mean values are Hermitian (or self-adjoint)

                      -  Eigenvalues are real

                   -  Eigenvectors with different eigenvalues are orthogonal   

       10.5.C Observable Operators  

        10.5.D Operators no associated to mean values

 10.6  The commutator 

       10.6.A  Expression for the generalized uncertainty principle

      10.6.B  Conjugate observables

                   Standard deviation of two conjugate observables

       10.6.C  Properties of operators that do commute

 10.7  How to prepare the initial quantum states

       10.7.A  Knowing a state what can we predict about eventual outcomes from measurement?

       10.7.B  After a measurement, what can we say about the current state  ?

       10.7.C  Simultaneous measurement of observables

                      10.7.C1  Definition of compatible (or simultaneously measurable) operators

                   10.7.C2  Condition for observables   and   to be compatible

                   10.7.C3  Complete set of commuting operators

References

Feynman Lectures Vol. III; Chapter 16, 20 "Introduction to Quantum Mechanics" by David Griffiths; Chapter 3. B. H. Bransden & C. J. oachin, “Quantum Mechanics”, Prentice Hall, 2nd Ed. 2000