110318 - 1 CHM3400 Lecture 27 – Mar 18 Schroedinger wave...

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Unformatted text preview: 1 CHM3400 - Lecture 27 – Mar 18 Schroedinger wave equation (Chapter 11 416-426) • Wave equations • Particle in a 1-D box • comparison to hydrogen atom and molecular case 2 Schroedinger equation ψ ψ ψ π E V dx d m h = + − 2 2 2 2 8 Kinetic energy Potential energy Total energy Time-independent Schroedinger equation in one dimension (x): ψ = wavefunction Unacceptable wavefunctions: Well-behaved wavefunction: 1. ψ must be single-valued at any point 2. ψ must be finite 3. ψ must have a smooth and continuous function 3 Particle in a 1-D box Imagine particle in a 1-D box with infinite potential barriers: ψ ψ π E dx d m h = − 2 2 2 2 8 Potential V = 0 in box ∞ ∞ Total energy is kinetic energy only: What E and ψ are allowed for such an equation? ) cos( ) sin( kx B kx A + = ψ Boundary conditions: ) ( ) ( = = L ψ ψ sin(0) = 0 and cos(0) = 1, if ⇒ B =0 ) cos( ) sin( ) ( = + = kx B kx A ψ 4 ) sin( kx A = ψ ψ ψ π E dx d m h = − 2 2 2 2 8 Particle in a 1-D box )...
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This note was uploaded on 05/29/2011 for the course CHM 3400 taught by Professor Seabra during the Spring '08 term at University of Florida.

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110318 - 1 CHM3400 Lecture 27 – Mar 18 Schroedinger wave...

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