Quantum Mechanics Postulates and Problem Set for Chem 455A, Spring 2008 - Prof. William Re, Assignments of Physical Chemistry

Download Quantum Mechanics Postulates and Problem Set for Chem 455A, Spring 2008 - Prof. William Re and more Assignments Physical Chemistry in PDF only on Docsity! Chem 455A Spring 2008 Reinhardt & Stanich Reading Assignment #5 (SAME as #4…this material takes some time to absorb!) We are now getting into more modern quantum theory: READ McQ, 2nd ED: p 97-103……do look at MathChapter A in preparation for review of complex numbers and functions for Thursday tutorial. Read Engel Ch 3 sections 1,2,3…note that Chapter 2 of Engel is a bit ahead of where we will be going on WED and Friday…. First (preliminary) statement of “postulates” for wave mechanics, we will be discussing these on WED and FRIDAY, see also Lecture #5 slide: 1) At any instant of time, maximal knowledge of a physical system is contained in knowledge of “the wave function” of that system. The absolute value “squared” of this wavefunction is related to the probability of observing the system at specific values of the co-ordinates of particles in the system 2) “Observables” (i.e. the results of measurements) are represented by “operators” in quantum mechanics 3) Possible values of “observables” are the eigenvalues of the corresponding operators 4) Average values of “observables” follow from an appropriate average over the wavefunction, which must be normalized to unit probability. Problem Set #5….due Monday April 14, 2008, due “in class (hand to Cynthia!), or in Box #56 by 5pm (Bagley closes at 5pm on Fridays), or give to Cynthia at the end of office hours on Friday (MGH 206), by 5:30. A) work out Examples 3-1, 3-2, 3-3 and 3-5 (NOT 3-4, yet) in McQ chapter 3, carrying out all steps, and checking that you agree with the work shown by McQ. Then: B) Work problems 3-2, 3-4, and 3-6 pages 120-121 in McQ C) Additional problem: do the operators (a) and (b) of problem 3-5, p 121, commute? If yes, demonstrate this, if not, what is the value of the “commutator”? Remember to “apply the operators” to an arbitrary function of x, say f(x).