LYCOS RETRIEVER 
Schrodinger Equation: Solutions
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The multiparticle Schrodinger equation is the basic governing equation in quantum mechanics, and ... the foundation for much of chemistry and physics. A tremendous amount of effort, over several decades, has gone into approximating its solutions, but high quality numerical solutions have proved elusive. Recently developed mathematical tools for computing in high dimensions have revealed a new path toward such solutions, which this project will explore. Such solutions will enable accurate computation of chemical and physical properties of molecules and materials, and thus have an impact on many problems in chemistry, physics, biology, and materials science.
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Since the Schrodinger equation only has solutions for certain values of the energy, the wave function shown is not necessarily a solution. Examine the edges of the displayed portion of the function - these should be tending towards zero for a solution.
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By switching to the Hydrodynamic formulation of the Schrodinger equation (Madelung's Transform), one obtains a means of calculating analytically approximate solutions to the time dependent Schrodinger equation. One application of this is Blip formation (see [1] for technical details).
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In this lab, the students find solutions to the one dimensional time independent Schrodinger equation using software that employs a fourth order Runge-Kutta numerical integration method. Where possible, they are asked to compare the results to theory or other known values.
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The program solves the one dimensional Schrodinger equation numerically to any desired degree of accuracy. The solutions are needed in molecular spectroscopy, molecular scattering theory and photodissoci- ation theory. They may ... be used as a component of a more extensive code for solving the Schrodinger equation in more than one dimension.
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The applet uses the fourth order Runge-Kutta method to numerically integrate the Schrodinger equation. Solutions are found by bisection; where neither interval is guaranteed to contain a solution (multiple solutions or no solution), the interval containing the previously selected energy value is chosen as a guess.
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