Introduction to Quantum Chemistry 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 Thu, 01 Jun 2006 13:47:57 -0400 Thu, 01 Jun 2006 13:47:57 -0400 Michelle Francl, Ph.D. Physical Chemistry Lectures at Bryn Mawr College quantum mechanics chemistry lasers Michelle Francl mfrancl@brynmawr.edu No The last lecture http://chemistry221.blogspot.com/2005/11/last-lecture.html Thu, 01 Jun 2006 13:47:57 -0400 the-last-lecture Michelle M Francl In which we say good-bye...and consider how a laser "amplifies" light. In which we say good-bye...and consider how a laser "amplifies" light. The truly dedicated student can build a laser by following the directions at Sam's Laser site. Lasers can be built from a number of different materials, including Jello! quantum chemistry lasers 19:10 Fiat Lux! Population inversion is the key to successful lasing http://chemistry221.blogspot.com/2005/11/fiat-lux-population-inversion-is-key.html Thu, 01 Jun 2006 13:46:08 -0400 fiat-lux-population-inversion-is-the-key-to-successful-lasing Michelle M Francl Where does the "SE" part of the word laser come from? Population inversion is a key feature of a system which be used to construct a laser. A system in thermal equilibrium follows Boltzmann's statistics, in which the number of molecules in higher energy states is smaller than the number in the lowest energy state. Lasers require that you have a non-equilibrium situation established, in which more molecules are "stuck" in an excited state than are currently in a lower energy state. This phenomenon is called population inversion. A second feature of lasers is that the emission process(the release of a photon when a molecule or atom relaxes from an excited state to a lower energy state) can be stimulated, or enhanced by the emissions from other molecules. This is where the "se" in the name comes from! (LASER = Light Amplification by Stimulated Emission of Radiation). 39:06 Lumos! The Quantum Mechanics of Harry Potter http://chemistry221.blogspot.com/2005/11/lumos-quantum-mechanics-of-harry.html Thu, 01 Jun 2006 13:44:16 -0400 lumos-the-quantum-mechanics-of-harry-potter Michelle M Francl Lasers are magic wands for chemists. And at last, the answer to the "burning" questions about CDs! We wrap up NMR and begin to consider the quantum mechanics behind lasers. Lasers are magic wands for chemists, making it possible to explore what happens in chemical processes on very short time scales. Lasers are ubiquitous tools in everyday life, too. Grocery store scanners and CD players use lasers to read information, an when you "burn" a CD, a laser is used to literally score the material. harry potter lasers quantum chemistry 35:23 A Pocket NMR? http://chemistry221.blogspot.com/2005/11/pocket-nmr.html cow magnet. It could be done, if you're not interested in very high resolution. ]]> Thu, 01 Jun 2006 13:41:41 -0400 a-pocket-nmr Michelle M Francl Could you build an NMR that could fit in your pocket? Could you build an NMR that could fit in your pocket? The effect of magnetic field on the splitting between nuclear spin states. What would happen if you walked through a very strong magnetic field? Say a million Tesla field? Are there such fields? We propose building a pocket-sized NMR from a cow magnet. It could be done, if you're not interested in very high resolution. 46:39 Magnetic Personalities: NMR http://chemistry221.blogspot.com/2005/11/magnetic-personalities-nmr.html Thu, 01 Jun 2006 13:16:34 -0400 magnetic-personalities-nmr Michelle M Francl Why are MRI magnets so strong they can suck up a desk chair? The quantum mechanics of nuclear spins. How a magnetic field splits degenerate spin states of at nuclei, setting the stage for NMR. Why do MRI machines need such strong magnets? What's a cow magnet? nmr mri quantum mechanics chemistry 34:22 Degrees of Freedom http://chemistry221.blogspot.com/2005/11/degrees-of-freedom.html mfrancl@brynmawr.edu (Michelle M Francl) Fri, 11 Nov 2005 16:07:31 -0500 degrees-of-freedom Michelle M Francl Hot bands and degrees of freedom. The vibrational spectra of most molecules is very complex. We considered how additional lines arise in diatomic spectra including isotopic substitution and "hot bands". There are many more vibrational modes available to polyatomic molecules. How many? 3N-6! vibrational spectroscopy quantum chemistry 48:14 A Matter of Moment http://chemistry221.blogspot.com/2005/11/matter-of-moment.html mfrancl@brynmawr.edu (Michelle M Francl) Wed, 09 Nov 2005 14:01:26 -0500 a-matter-of-moment Michelle M Francl What types of molecular tops are there? The rotation of polyatomic molecules. The rotational spectra of polyatomic molecules depend on the moments on inertia about the principal axes. We considered 4 cases: linear molecules, spherical tops, oblate symmetric tops and prolate symmetric tops. We backtracked to vibration spectroscopy to discuss the Franck-Condon principle, or the principle of vertical excitation. It adds a third rule to our list: What goes up must come down; You can't always get there from here; When you go up, go straight up! quantum chemistry rotational spectrscopy oblate prolate 40:36 Shake, Rattle and Roll: Simultaneous Excitation of Vibrational and Rotational States http://chemistry221.blogspot.com/2005/11/shake-rattle-and-roll-simultaneous.html mfrancl@brynmawr.edu (Michelle M Francl) Wed, 09 Nov 2005 14:02:03 -0500 shake-rattle-and-roll-simultaneous-excitation-of-vibrational-and-rotational-states Michelle M Francl Why are there all those lines in the HCl spectrum? Why is there no line at the fundamental frequency? We consider the interplay of rotation and vibration and their respective selection rules to see why. Why are there all those lines in the HCl spectrum? Why is there no line at the fundamental frequency? We consider the interplay of rotation and vibration and their respective selection rules to see why. quantum chemistry spectroscopy rotation vibration Out of Tune: The Effects of Anharmonicity and Centrifigual Distortion on Rotational/Vibrational Spectra http://chemistry221.blogspot.com/2005/11/out-of-tune-effects-of-anharmonicity.html mfrancl@brynmawr.edu (Michelle M Francl) Mon, 07 Nov 2005 08:53:36 -0500 out-of-tune-the-effects-of-anharmonicity-and-centrifigual-distortion-on-rotationalvibrational-spectra Michelle M Francl What are overtones? Anharmonic oscillation. We noted in our demonstration on Friday that rotation affected vibration. We quantified this, including a term in the energy to account for centrifugal distortion. The effect is small, but noticeable, as we saw with HCl. We consider the appearance of overtones in the vibrational spectrum, and the shifts in equilibrium bond length that occur as a result of the anharmonicity of the vibrational potential. quantum chemistry spectroscopy anharmonic 47:01 Pure Vibrational Spectroscopy http://chemistry221.blogspot.com/2005/11/pure-vibrational-spectroscopy.html mfrancl@brynmawr.edu (Michelle M Francl) Wed, 02 Nov 2005 08:49:49 -0500 pure-vibrational-spectroscopy Michelle M Francl Where did all those lines come from? We consider selection rules for pure vibrational spectroscopy. Using the harmonic oscillator to model vibrational energy transitions can be done, but has its limits. Consider the observed high resolution spectrum of gaseous HCl. vibrational spectroscopy quantum mechanics chemistry 34:50 An Exciting Lecture: An Introduction to Molecular Spectroscopy http://chemistry221.blogspot.com/2005/10/exciting-lecture-introduction-to.html mfrancl@brynmawr.edu (Michelle M Francl) Tue, 01 Nov 2005 14:53:36 -0500 an-exciting-lecture-an-introduction-to-molecular-spectroscopy Michelle M Francl Why does your white shirt glow under a blacklight? What makes the glow in the dark stars glow? How does a glow stick work? It's all spectroscopy! Why does your white shirt glow under a blacklight? What makes the glow in the dark stars glow? How does a glow stick work? We look at the absorbtion and emission of light by molecules. This is an appropriate lecture for Halloween since the first meaning of "spectrum" is "ghost". spectroscopy spectrum quantum mechanics chemistry 43:49 Spinning Around: The Pauli Principle and Slater Determinants http://chemistry221.blogspot.com/2005/10/spinning-around-pauli-principle-and.html Some biographical information on J.C. Slater]]> mfrancl@brynmawr.edu (Michelle M Francl) Fri, 28 Oct 2005 14:08:59 -0400 spinning-around-the-pauli-principle-and-slater-determinants Michelle M Francl Do electrons really spin? How can we build a wavefunction for a molecule from the solutions to the hydrogen atom? Electron spin is generally viewed as an ad hoc development in wave mechanics (though it arises naturally in other forumations, such as Dirac's). Using a general statement of the Pauli Exclusion Principle, we showed that Slater's suggestion of using wavefunctions constructed from determinants would insure that the Pauli's principle was satisfied. quantum chemistry electron spin pauli principle slater determinant 44:34 Linear Variation Theory: Building a Better Wavefunction Piece by Piece http://chemistry221.blogspot.com/2005/10/linear-variation-theory-building.htm mfrancl@brynmawr.edu (Michelle M Francl) Wed, 26 Oct 2005 12:48:31 -0400 linear-variation-theory-building-a-better-wavefunction-piece-by-piece Michelle M Francl Using linear combinations of "off the shelf" functions to build a better wavefunction. quantum chemistry variation theory 18:20 Using Variational Theory http://chemistry221.blogspot.com/2005/10/using-variational-theory.html mfrancl@brynmawr.edu (Michelle M Francl) Wed, 26 Oct 2005 12:37:35 -0400 using-variational-theory Michelle M Francl How to use a variational parameter to get the best variational energy. How to use linear combinations of functions. Different trial functions yield different energies, the quality of the energy doesn't necessarily predict the quality of other properites predicted from the wavefunction (such as average position). We looked at the framework for linear variation theory, since this is the backbone of one of the standard methods for computational molecular quantum chemistry. quantum mechanics chemistry particle sphere 42:48 Variational Theory Test Drive http://chemistry221.blogspot.com/2005/10/test-drive-of-variational-theorem.html mfrancl@brynmawr.edu (Michelle M Francl) Mon, 24 Oct 2005 11:58:29 -0400 variational-theory-test-drive Michelle M Francl Does better at computing the energy mean better overall? A Mathematica exercise based on the one-dimensional particle in the box explores the variational principle. Does a function with a lower energy necessarily do better at predicting other quantities, such as the average position of the particle within the box? variational theory quantum mechanics 8:34 Variations on a Theme http://chemistry221.blogspot.com/2005/10/variations-on-theme.html gaussian function can be used to find an approximation to the wavefunction and the energy. ]]> mfrancl@brynmawr.edu (Michelle M Francl) Wed, 19 Oct 2005 12:38:06 -0400 variations-on-a-theme Michelle M Francl Using the variational theorem to find the wavefunctions and energies for a system. Though the Schrodinger equation cannot be solved exactly, robust approximate techniques exist for finding solutions to problems of interest to chemist. The variational theorem is the foundation for much of computational chemistry. Using a Mathematica notebook we explore how a simple gaussian function can be used to find an approximation to the wavefunction and the energy. variation theory quantum chemistry 48:08 2s Orbitals Really are Bigger than 2p and other Urban Legends of Atomic Orbitals Debunked http://chemistry221.blogspot.com/2005/10/2s-orbitals-really-are-bigger-than-2p.html mfrancl@brynmawr.edu (Michelle M Francl) Mon, 17 Oct 2005 15:45:40 -0400 2s-orbitals-really-are-bigger-than-2p-and-other-urban-legends-of-atomic-orbitals-debunked Michelle M Francl What measures do chemists use for orbital size and how are they computed using quantum mechanics? We introduced multi-electron atoms: He. The problem? It can't be solved! Why? Electron-electron repulsion makes the Hamiltonian inseparable. How big is an orbital? What measures do chemists use for orbital size and how are they computed using quantum mechanics? Why would an orbital on carbon be smaller than one on lithium? Is is purely an electrostatic effect, or would the presences of other electrons change the sizes? How? We introduced the first multi-electron atomic system we will study: He. The problem? It can't be solved! Why? Electron-electron repulsion makes the Hamiltonian inseparable. helium atom quantum chemistry orbitals 47:29 The Mystery of s,p,d and f Revealed http://chemistry221.blogspot.com/2005/10/mystery-of-spd-and-f-revealed.html L2. Knowing that linear operators that commute share at least one set of eigenfunctions, we tested to see if the Hamiltonian and L2 did commute. They do, and so there must exist a common set of eigenfunctions. Since we already know one set of eigenfunctions for angular momentum operator, the the spherical harmonics or Yl,m, we tried a solution to the one-electron atom Schrodinger equation of the form R(r)Yl,m(θ,φ). Such solutions do work and allow us to derive a differential equation in a single variable, r, to solve for the radial part of the wavefunction. We talked about the origins of the familiar orbital designations, s, p, d nd f.
See rotatable images of s, p, d, f and g orbitals.]]> mfrancl@brynmawr.edu (Michelle M Francl) Wed, 05 Oct 2005 13:32:12 -0400 the-mystery-of-spd-and-f-revealed Michelle M Francl Where do the designations s, p, d and f come from? We rewrote the Hamiltonian for a one-electron atom in terms of the operator L2. Knowing that linear operators that commute share at least one set of eigenfunctions, we tested to see if the Hamiltonian and L2 did commute. They do, and so there must exist a common set of eigenfunctions. Since we already know one set of eigenfunctions for angular momentum operator, the the spherical harmonics, we tried a solution to the one-electron atom Schrodinger equation of the form R(r)Yl,m. Such solutions do work and allow us to derive a differential equation in a single variable, r, to solve for the radial part of the wavefunction. We talked about the origins of the familiar orbital designations, s, p, d nd f. See rotatable images of s, p, d, f and g orbitals at http://www.d.umn.edu/~pkiprof/ChemWebV2/index2.html. quantum chemistry hydrogen atom orbitals 42:33 Morphing Quantum Spheres into Atoms: The Spherical Harmonics and Associated Legendre Functions http://chemistry221.blogspot.com/2005/10/morphing-quantum-spheres-into-atoms.html 2. The eigenfunctions of this operator are well known and called the spherical harmonics or Yl,m. We noted that the solutions depended on two quantum numbers, l and ml. We wrote down the Hamiltonian for a one-electron atom (the archetype would be the hydrogen atom) and discussed the form of the potential energy (Coloumbic or electrostatic attraction). We noted that we could simplify matters by assuming that nuclear motion was very slow compared to the motion of the electrons and therefore could be (to a first approximation) ignored. ]]> mfrancl@brynmawr.edu (Michelle M Francl) Mon, 03 Oct 2005 12:38:34 -0400 morphing-quantum-spheres-into-atoms-the-spherical-harmonics-and-associated-legendre-functions Michelle M Francl As a step along the path to creating a quantum mechanical model of an atom, we considered the solution to the problem of a single particle moving on the surface of a sphere. As a step along the path to creating a quantum mechanical model of an atom, we considered the solution to the problem of a single particle moving on the surface of a sphere. We saw that the Hamiltonian for the motion could be written simply in terms of the angular momentum operator. The eigenfunctions of this operator are well known and called the spherical harmonics. We noted that the solutions depended on two quantum numbers, l and ml. We wrote down the Hamiltonian for a one-electron atom (the archetype would be the hydrogen atom) and discussed the form of the potential energy (Coloumbic or electrostatic attraction). We noted that we could simplify matters by assuming that nuclear motion was very slow compared to the motion of the electrons and therefore could be (to a first approximation) ignored. quantum mechanics chemistry particle sphere 45:37 Around and around in circles: the rigid rotor http://chemistry221.blogspot.com/2005/09/around-and-around-in-circles-rigid.html mfrancl@brynmawr.edu (Michelle M Francl) Mon, 03 Oct 2005 09:17:08 -0400 around-and-around-in-circles-the-rigid-rotor Michelle M Francl Meet a wavefunction that has imaginary values! The rotation of simple diatomic molecules can be modeled quantum mechanically by the movement of a particle on a ring. Meet a wavefunction that has imaginary values! The rotation of simple diatomic molecules can be modeled quantum mechanically by the movement of a particle on a ring. We consider one more model problem, this one concerning the rigid rotation of a diatomic molecule. Though the problem is simple compared to most molecular systems chemists are interested in, it yielded our first example of a wavefunction that was complex and not real valued. It will also provide a basis for an atomic model problem - the hydrogen atom. quantum chemistry rigid rotor 38:01 Quantum Mechanical Escapes: Tunneling Through Walls http://chemistry221.blogspot.com/2005/09/quantum-mechanical-escapes-tunneling.html mfrancl@brynmawr.edu (Michelle M Francl) Tue, 27 Sep 2005 10:31:32 -0400 quantum-mechanical-escapes-tunneling-through-walls Michelle M Francl What happens when you shoot an electron at a wall? It can go right through! What happens when you shoot an electron at a wall? We consider the case of a particle impinging on a rectangular potential barrier to discover that under many conditions - the particle goes right through! An electron with an energy of 4 eV has about a 70% chance of going "through" a 5eV wall and coming out the other side. quantum chemistry harmonic oscillator tunneling 12:22 Overstepping the boundaries: Harmonic Oscillators Defy the Classical Limits http://chemistry221.blogspot.com/2005/09/overstepping-boundaries-harmonic.html mfrancl@brynmawr.edu (Michelle M Francl) Tue, 27 Sep 2005 08:56:32 -0400 overstepping-the-boundaries-harmonic-oscillators-defy-the-classical-limits Michelle M Francl Quantum mechanics predicts that oscillators can reach beyond the classical boundaries. How can parity work for you in quantum mechanics? We see that the parity of the harmonic oscillator solutions can make some problems trivial (the average value of the position, for example). We computed the probability of a harmonic oscillator being stretched or compressed further than classical mechanics would permit, to discover that in the ground state of HCl the probability was 15% that the classical limits would be exceeded. quantum chemistry harmonic oscillator 49:56 Shaking Things Up: The Harmonic Oscillator http://chemistry221.blogspot.com/2005/09/shaking-things-up-harmonic-oscillator.html mfrancl@brynmawr.edu (Michelle M. Francl) Wed, 21 Sep 2005 15:21:54 -0400 shaking-things-up-the-harmonic-oscillator Michelle M. Francl How do chemists know what molecule they've made and how quantum chemistry can help! Moving beyond the particle in the box, a model for simple molecular vibrations is constructed. The solutions depend on the Hermite polynomials and exhibit parity. Wavefunctions for states with an even quantum number have even parity (are symmetric about the y axis) and those with odd quantum numbers are odd. Parity considerations can simplify quantum chemical calculations. quantum chemistry 49:30 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 14:30:09 -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) Fri, 16 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