SCHROEDINGER EQUATION

In the middle of the preceding slide the line should read

Momentum and energy are classical concepts. The quantum mechanical equivalents are ``operators'' which we do not study in detail this year. Operators are written with a ^ on top of the letter. We just need to know what are the ``operators'' for some common quantities:

The Schroedinger Equation is the basic equation of Quantum Mechanics. We are going to study it as follows:
  1. Remove the time-dependence and create the time-independent Schroedinger equation.
  2. Study the solution in an infinite one-dimensional square box or well.
  3. Study the solution in a finite one-dimensional square box or well.
  4. Study the solution in an infinite three-dimensional box, first separating the equations into three variables. We will learn about degeneracy.
  5. Study the solution for a parabolic well - this is a quantum harmonic oscillator.
  6. Study what happens when there is a step, or barrier - the tunneling effect and its applications.
  7. Then we move to spherical coordinates and study the solution for the hydrogen atom.

See a picture and movies of the Schroedinger Equation solutions. (These are downloadable mpeg files.) The full movie can be downloaded in two parts part I and part II

There is also an interactive matlab solver for the Schroedinger equation, prepared by Dany Regelman. It can be downloaded here .

The last equation above has the capital psi replaced by the product of small psi and phi. In the line below, both sides are divided by this product, but there is a typo which is an extra uneeded phi on the top of the first term of the middle expression.


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PHYSICS 3- HOMEPAGE