Welcome to the Chem 373 Sixth Edition + Lab Manual It is all on the web !!

Lecture 1: Classical Mechanics and the Schrödinger Equation This lecture covers the following parts of Atkins 1. Further information 4. Classical mechanics (pp ) The Schrödinger Equation (pp 294) Lecture-on-line Introduction to Classical mechanics and the Schrödinger equation (PowerPoint) Introduction to Classical mechanics and the Schrödinger equation (PDF) Handout.Lecture1 (PDF) Taylor Expansion (MS-WORD)

Tutorials on-line The postulates of quantum mechanics (This is the writeup for Dry-lab-II)( This lecture has covered (briefly) postulates 1-2)(You are not expected to understand even postulates 1 and 2 fully after this lecture) The Development of Classical Mechanics Experimental Background for Quantum mecahnics Early Development of Quantum mechanics The Schrödinger Equation The Time Independent Schrödinger Equation

Audio-Visuals on-line Quantum mechanics as the foundation of Chemistry (quick time movie ****, 6 MB) Why Quantum Mechanics (quick time movie from the Wilson page ****, 16 MB) Why Quantum Mechanics (PowerPoint version without animations) Slides from the text book (From the CD included in Atkins,**)

or Linear Momentum and Kinetic Energy The kinetic energy can be written as : Or alternatively in terms of the linear momentum: as:

A particle moving in a potential energy field V is subject to a force Force in one dimension Force in direction of decreasing potential energy

Potential energy V The force has the direction of steepest descend Force F

The expression for the total energy in terms of the potential energy and the kinetic energy given in terms of the linear momentum The Hamiltonian will take on a special importance in the transformation from classical physics to quantum mechanics is called the Hamiltonian

Quantum Mechanics The particle is moving in the potential V(x,y,z) Classical Hamiltonian We consider a particle of mass m,

Classical Hamiltonian The classical Hamiltonian is given by

Quantum Mechanical Hamiltonian

We have Thus

Contains all kinetic information about a particle moving in the Potential V(x,y,z)

The position of the particle is a function of time. Let us assume that the particle at has the position and the velocity What is By Taylor expansion around or

However from Newtons law: Thus :

At the later time :we have The last term on the right hand side of eq(1) can again be determined from Newtons equation as

We can determine the first term on the right side of eq(1) By a Taylor expansion of the velocity Where both:and are known

The position of a particle is determined at all times from the position and velocity at t o