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Readings
Atkins Chapter 28, 558-565
S&Z Chapter 18, 419-424
Activity 6, Waves of Matter, VQM Activities
In Module C we examined the behavior of electrons and discovered that they can have wave properties. We introduced the idea of a wavefunction for describing the electron. The wavefunction is useful because it can tell us the probability of finding an electron in a certain location at a certain point in time. In Module D we looked at how we could describe an objects behavior in terms of potential and kinetic energies using an energy diagram.
In this module we will learn how to sketch a wave function given specific energy parameters. This will be very useful when we want to predict an electron's behavior in certain situations (e.g. an electron in an atom, an electron in a molecule or a crystal, a free electron).
When physicists wish to describe or predict the motion of large objects, they work with some basic concepts such as Newton's Laws. They consider the forces or energies involved, then write equations, draw graphs and predict changes as the object moves through time and space.
Predicting probabilities for small objects is somewhat similar. The basic concept is Schrödinger's Equation named for Erwin Schrödinger who first wrote it. This equation describes the changes in wave functions over space and time. It is based on the wave behavior of small objects and conservation of energy.
The mathematical form of Schrödinger's Equation is a little
complex, so we will not spend time solving it analytically for
each case that interests us, instead we will introduce a series
of steps based on the equation. These steps will enable you to
sketch wave functions for several situations, then interpret the
results in terms of probabilities.