Lecture3Ch161Feb2

Lecture3Ch161Feb2 - Section Times: Monday 5pm-6pm Cabot...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
• Section Times: • Monday 5pm-6pm Cabot Division Rm Mallincrodt 102 • Tue 2pm-3pm M217 Chemistry Dept Midterm Exam – March 9.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Lessons from the random walk example Description in terms of exact sequence of steps is extremely counterproductive: There is a huge number of equally probable possibilities (and frankly we do not care about exact sequence of steps taken by a drunk!) Then we switched to a coarse-grained description: we are interested only in total number of steps to the right and steps to the left taken regardless of their exact order- I.e we switched from microscopic to macroscopic description of the problem . It gave us a huge advantage because these microscopic quantities are observables - they tell us where to collect random walkers. The key point though is that while each sequence of steps is equally probable, the distribution in terms of macroscopic parameters is sharply peaked around the average value of Nr - making Nr self-avergaing In converting from ‘’microscopic description’’ to macroscopic description we had to count the number of paths giving rise to a given Nr, N l (binomial coefficients) - I.e we introduced the concept of ENTROPY
Background image of page 2
Chemistry 161: Statistical Chemistry 161: Statistical Thermodynamics Thermodynamics Lecture 3: Lecture 3: Statistical Description of Many particle Statistical Description of Many particle Systems Systems Key Concepts and Lessons: a) Phase Space b) Density of States c) Main postulate of SM Reading: Reif, Ch2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
I. State of the system A large number of particles forms a macroscopic assembly called the system The most exhaustive quantum description of a state of the system consisting of N particles is given by its wavefunction As we already know such description is hardly possible for huge numbers of particles. An alternative (and more complete) macroscopic description of the system is in terms of quantum numbers. Quantum numbers give detailed description of quantum system given quantum symmetries. ! r q 1 , r q 2 .... r q N ( )
Background image of page 4
Quantum Numbers- Examples and Lessons The simplest – and useful - example is set of particles (e.g. electrons, nuclei etc) which carry spin ½ Each such particle is characterized by the azimutal quantim number m z which can take only two values ‘’up’’, i.e. +1/2 and ‘’down’’ i.e. -1/2. Now consider N such particles. A possible state of the system is then (-1/2,-1/2,1/2…….-1/2).
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Example 2: An Ensemble of Oscillators Another example is a system of N harmonic oscilllators. Each H.O can be described by quantum number n which specifies its state (and its wave function as well). For the ensemble of N H.O the most complete description would be set of quantum numbers n for each H.O. (n 1, n 2, n 3…… n N ). Total energy of the system (we will see later that it is a very important characteristic) is then E tot = h ! n
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/04/2010 for the course CHEM 161 taught by Professor Shaklovich during the Spring '10 term at Harvard.

Page1 / 36

Lecture3Ch161Feb2 - Section Times: Monday 5pm-6pm Cabot...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online