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The Schr&Atilde;&para;dinger Equation

# The Schr&Atilde;&para;dinger Equation - The...

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The Schrödinger Equation Ch 301 B. A. Rowland September 8, 2008

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A Brief Review Experiments have shown that matter has a wave-particle duality. We briefly examined the Schrödinger Equation as a new governing equation for chemistry. This equation explicitly brings in this duality as we will be solving the system for a wave (the wave function). The wave function Ψ represents everything knowable about a system. Today: How do we generate solutions to the TISE?
The Schrödinger Equations We now have learned that matter will sometimes behave as a wave—we need a new governing equation in chemistry! In 1926 Schrödinger proposes two equations for this purpose. Schrödinger introduces ψ to represent the wave function of the system. H is an operator (not a variable) which is unique for each atom. 2200 Ψ can be thought of as the function that contains all the information that can be known about the system—it is a wave! ˆ i t ψ ψ = Η h ˆ E ψ ψ Η = Time-Dependent Schrödinger Equation My work in graduate school was to find Ways to solve this equation for systems. Interesting equation, but not our focus. Time-Independent Schrödinger Equation This equation will be our focus.

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Coulomb’s Law Charged particles (protons and electrons) interact via Coulomb’s Law. Electrostatic interactions can be used to describe a great deal of chemistry.
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The Schr&Atilde;&para;dinger Equation - The...

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