Chemistry221 http://Chemistry221.blogspot.com Audio feed of lectures in introductory physical chemistry at Bryn Mawr College. Why are Cheetos orange and flamingos pink? Why do they call it "burning" a CD? Are pi orbitals real? The answers to these questions and more! Feeder 1.2.1 http://reinventedsoftware.com/feeder/ http://blogs.law.harvard.edu/tech/rss en-us c. 2005 Michelle M. Francl mfrancl@brynmawr.edu mfrancl@brynmawr.edu Mon, 19 Sep 2005 13:33:32 -0400 Mon, 19 Sep 2005 13:33:32 -0400 Michelle Francl, Ph.D. Physical Chemistry Lectures at Bryn Mawr College quantum mechanics chemistry lasers Michelle Francl mfrancl@brynmawr.edu No The Real Product: Particle in a 3-Dimensional Box http://chemistry221.blogspot.com/2005/09/real-product-particle-in-3-dimensional.html Mathematica notebook - same as previous lecture
Trout Fishing in America - the band Six
What do you get when you add three plus three? I believe the answer is six. And how ‘bout seven when take away one now? I believe the answer is six. Well, how do you do that in your head? I would need a pencil all filled with lead, A huge piece of paper ‘bout the size of my bed. Now…You must be a mathematician.....
and on...to
What is the dimension of the field of complex numbers over the real numbers, times the order of the alternating group on three elements divided by the definite integral from zero to pi over two of sine of X D X?
]]> mfrancl@brynmawr.edu (Michelle M. Francl) Mon, 19 Sep 2005 13:24:03 -0400 the-real-product-particle-in-a-3dimensional-box Michelle M Francl We show that the product of one-dimensional functions is indeed a solution to the 3-dimensional problem. We find the energy and show that the energy and wavefunction now depend on 3 independent quantum numbers. When the box is symmetric, for example, a cube, some energy levels are degenerate. We noted that symmetry generally leads to degeneracy, though not all degeneracy is a result of symmetry (accidental symmetry). We extended the concept of the product wavefunction to systems of more than one particle. We drew a quick concept map of where we have been in the course so far. symmetry degeneracy quantum mechanics chemistry 49:20 Particles in Real Boxes http://chemistry221.blogspot.com/2005/09/particles-in-real-boxes.html mfrancl@brynmawr.edu (Michelle M. Francl) Mon, 19 Sep 2005 13:10:36 -0400 particles-in-real-boxes Michelle M Francl How to reduce a 3-dimensional problem to three 1-dimensional problems we already know the answer to. A "real" quantum mechanical box - that is, one that is 3-dimensional. We consider the case of a particle confined to a rectangular parallelepiped. The Schrodinger equation for this system separates neatly into 3 one dimensional cases and we propose that the solutions to these problems are the 1-D particle in a box wavefunctions. We will verify this in the next lecture. three dimensional wavefunctions quantum chemistry mechanics 49:20 The wavefunction is a complete description of the system http://chemistry221.blogspot.com/2005/09/wavefunction-is-complete-description.html mfrancl@brynmawr.edu (Michelle M. Francl) Wed, 14 Sep 2005 12:41:33 -0400 the-wavefunction-is-a-complete-description-of-the-systemthe-wavefunction-is-a-complete-description-of-the-systemthe-wavefunction-is-a-complete-description-of-the-systemthe-wavefunction-is-a-complete-description-of-the-system Michelle Francl, Ph.D. What are the practical details involved in using the wavefunction to extract information about a system? Our first postulate of quantum mechanics is that the wavefunction is a complete description of the system. This is great in principle, but what are the practical details? How do we use the wavefunction to produce information that is useful to chemists? The difference between average (or expectation) values and the probability density are explored. We consider the radial distribution of electron density in 1s and 3s orbitals using Mathematica. quantum mechanics particle in a box wavefunction 41:15 What to "expect" from quantum mechanics? http://chemistry221.blogspot.com/2005/09/what-to-expect-from-quantum-mechanics.html mfrancl@brynmawr.edu (Michelle M. Francl) Fri, 09 Sep 2005 13:24:31 -0400 what-to-expect-from-quantum-mechanics Michelle M. Francl Orthonormality and the probability density. How can we use the framework of quantum mechanics to tell us something useful to chemists? The expectation value and the probability density are the keys. The eigenfunctions of the Hamiltonian are an orthonormal set. We graphed the probability density and wavefunctions for the particle in the box. We noticed that as n increased, the probabilty profile appeared more classical - a manifestation of the Bohr Correspondance Principle. quantum mechanics expectation values Mathematica 30:56 Making Up the Rules: Three Postulates of Quantum Mechanics http://chemistry221.blogspot.com/2005/09/making-up-rules-three-postulates-of.html mfrancl@brynmawr.edu (Michelle M. Francl) Wed, 07 Sep 2005 15:04:33 -0400 making-up-the-rules-postulates-of-quantum-mechanics What is the role of the operator in quantum mechanics? How are operators created? A brief overview of the basics of operator algebra. Why doesn't the wavefunction just cancel out in the Schrodinger equation? Operators, rules that change one function into another, play a key role in quantum chemistry. Each measurable quantity has a corresponding operator, and the operator, used in tandem with the wavefunction, can be used to calculate expected values of these quantities. We introduced the notion of the wavefunction as a vector in a function space and used Dirac's bra and ket notation to express the wavefunction and the expectation value. operators dirac bra ket 46:23 Solving the Schrodinger Equation for a Confined Particle http://chemistry221.blogspot.com/2005/09/what-happens-when-you-confine-very_05.html mfrancl@brynmawr.edu (Michelle M. Francl) Mon, 05 Sep 2005 12:42:33 -0400 solving-the-schrodinger-equation-for-a-confined-particle Michelle Francl, Ph.D. Schrodinger's equation provides a way to describe the wave nature of matter, most important for the small bits of matter that concern chemists. We solve What happens when you confine a very small particle to a small area? Quantization, that's what. Schrodinger's equation provides a way to describe the wave nature of matter, most important for the small bits of matter that concern chemists. We solve Schrodinger's equation for a model problem of a particle in a 1-D universe, confined to a small line segment, to get the wave functions and the energy. The solution requires using the boundary conditions for the problem, including the condition that the total probability of finding the particle somewhere in the universe is 1. We notice that not every wavefunction of the proper form is allowed, nor is every energy. The solutions are characterized by a quantum number "n". particle box schrodinger equation normalization 46:56 The Rise of Quantum Mechanics http://chemistry221.blogspot.com/2005/09/rise-of-quantum-mechanics-schrodingers_02.html mfrancl@brynmawr.edu (Michelle M. Francl) Fri, 02 Sep 2005 12:42:42 -0400 the-rise-of-quantum-mechanics Michelle Francl, Ph.D. Schrodinger's Wave Equation In late 1925 Erwin Schrodinger, prompted by a question asked by Sommerfeld in a seminar Schrodinger had given, developed the wave equation. I presented the 1-dimensional, time independent Schrodinger equation for a single particle. We set up a sample problem, for a single particle trapped in an infinitely deep potential energy well and found solutions (by inspection) for the wave equation in 3 different regions (outside the box, where it is zero, and inside the box). We discussed the basic form of the Hamiltonian operator. quantum mechanics chemistry wave equation 45:35 The Downfall of Classical Physics http://chemistry221.blogspot.com/2005/08/downfall-of-classical-physics-podcast.html mfrancl@brynmawr.edu (Michelle M. Francl) Mon, 29 Aug 2005 12:42:51 -0400 the-downfall-of-classical-physics Michelle Francl, Ph.D. How much of a disaster was the UV catastrophe? In the late 19th century the reputation of Newtonian physics with its ability to describe the macroscopic behavior of matter was beyond reproach. As the end of the century approached, scientists began to be able to make accurate observations of very small pieces of matter, such as atoms. Suddenly, the fabric of physics began to fray. What is the UV catastrophe? How much damage did it do and to who? quantum mechanics chemistry lasers 13:00