Quantum mechanics
Peer Led Team Learning Workshops


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http://quantum.bu.edu/PLTL/workshops.html
Updated Monday, August 16, 2010 3:54 PM

Copyright © 2005 Dan Dill (dan@bu.edu)
Department of Chemistry, Boston University, Boston MA 02215

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Here are the workshop titles. Click on a title to go to its brief description and to access the full workshop.

  1. Curvature based solution of Schrödinger equation
  2. Average values and uncertainties
  3. Momentum of a quantum particle and the Heisenberg uncertainty principle
  4. Series expansion—A Swiss army knife for calculations and analysis
  5. Particle on a ring
  6. Approximate energies and wave functions (in two parts)
  7. One-electron-atom orbitals
  8. Diatomic molecule vibrational and rotational spectra
  9. Rovibrational and rovibronic spectra of gaseous HCl


1: Curvature based solution of Schrödinger equation

A useful way of working with the Schrödinger equation is based on viewing it as a relation between the curvature of the wavefunction and kinetic energy. This workshop explores how to use this view accounts for the qualitative properties of wavefunctions and for energy quantization. [more... (PDF: 6 pages, 57 KB)]

2: Average values and uncertainties

The work of Bohr and de Broglie led to the idea that matter must be represented in terms of wavefunctions, and Born introduced the idea that the squared magnitude of a wavefunction at a point determines the probability that the object described by the wavefunction will be found at that point. This workshop explores how to use these ideas to predict the spatial position, momentum and energy (and their uncertainties) of a particle from its wavefunction. [more... (PDF: 6 pages, 69 KB)]

3: Momentum of a quantum particle and the Heisenberg uncertainty principle

In this workshop we will see how to compute particle properties that are represented as operators, and then explore the consequences of the position-momentum commutation relation on the simultaneous values of uncertainties of different particle properties. The most famous of these is the position-momentum (Heisenberg) uncertainty product. [more... (PDF: 7 pages, 66 KB)]

4: Series expansion—A Swiss army knife for calculations and analysis

In this workshop we will explore series expansions and how they are helpful in analyzing quantum mechanical expressions and carrying out calculations with them. This workshop is based in part on McQuarrie and Simon, Physical Chemistry (University Science Books, 1997), MathChapter I. My hope is that once you have digested this workshop, you will have some confidence that you can actually use series expansions to do certain kinds of calculations and analyses much more easily. [more... (PDF: 5 pages, 49 KB)]

5: Particle on a ring

A particle of mass m moving on a ring of radius r in the x y plane is an important model quantum system. It also provides nice examples of working with operators, the properties of their eigenfunctions and eigenvalues, and time dependence of wave functions. [more... (PDF: 3 pages, 46 KB)]

6: Approximate energies and wave functions

We have learned how to find wave functions and energies by adjusting the total energy so the wave function is decays to zero in forbidden regions of infinite width or infinite potential energy. In numerical applications of quantum mechanics in chemistry, an alternative, flexible method of solving the Schrödinger equation is to approximate the wave function for a particular system in terms of those for a similar, so-called model system. A very nice feature of this approach is that the accuracy of the approximation can be systematically improved, by increasing the number of model wave functions used in the approximation. In this workshop we'll explore this method, for the example of a particle confined to an infinite well with a sloping bottom. The model system will be the corresponding infinite well with a flat bottom. [more... (PDF: 12 pages, 104 KB)]

7: One-electron-atom orbitals

Three-dimensional wave functions of an electron in a one-electron atom are known as one-electron-atom orbitals. Electrons in many-electron atoms can be approximately represented in terms of these orbitals. The spatial properties of these orbitals are essential components in understanding the periodic properties of many-electron atoms, the bonding of diatomic molecules, and the shapes of polyatomic molecules. For these reasons it is important to be familiar with the three-dimensional structure of one-electron-atom orbitals. In this workshop you will explore the properties of these orbitals. [more... (PDF: 5 pages, 65 KB)]

8: Diatomic molecule vibrational and rotational spectra

We have learned how the adiabatic and Born-Oppenheimer approximations allow us to separate the electronic, vibrational, rotational and center of mass contributions to the energy of a diatomic molecule. The key result is simple expressions for the electronic, vibrational and rotational contributions to the internal energy of the molecule. The purpose of this workshop is become familiar with these energy contributions and to see how to use them to understand vibrational and rotational spectra. [more... (PDF: 5 pages, 54 KB)]

9: Rovibrational and rovibronic spectra of gaseous HCl

This workshop illustrates that rovibrational and rovibronic spectra of diatomic molecules are a rich source of information about their structure in their different electronic states. With experience, you will be able to tell with just a glance at a molecular spectrum quite a lot about the internal details of the molecule. [more... (PDF: 9 pages, 91 KB)]

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http://quantum.bu.edu/courses/ch351/workshops.html
Updated Monday, August 16, 2010 3:54 PM
Dan Dill (dan@bu.edu)