Lecture 4. : The Free Particle The material in this lecture covers the following in Atkins The informtion of a wavefunction (a) The probability density Lecture on-line Free Particle (PDF) Free Particle (HTML) Free Particle (PowerPoint) Tutorials on-line The postulates of quantum mechanics (This is the writeup for Dry-lab-II)( This lecture does not cover any specific postulate) Standing Wave (animation) (a must) The wave Packet as superposition of plane waves (annimation) (a must) A complete walk-through the free paricle (a must) The Development of Classical Mechanics Experimental Background for Quantum mecahnics Early Development of Quantum mechanics Audio-visuals on-line The dual nature of matter (Quick Time movie 9 MB from Wilson group, *** ) Linear polarized light ( a wave function in 1-D would propagate in a similar way) (1 MB Quick time movie from the Wilson Group, *****) Circular polarized light ( ( a wave function could propagate in a similar way) (6 MB Quick time movie from the Wilson Group, *****) Slides from the text book (From the CD included in Atkins,**)

The expression for the total energy in terms of the potential energy and the kinetic energy given in terms of the linear momentum: is called the Hamiltonian:

The total wavefunction for a one-dimentional particle in a potential V(x) is given by

1 We get for the probability density: Or

1 1