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Unformatted text preview: 1 CHM3400  Lecture 27 Mar 18 Schroedinger wave equation (Chapter 11 416426) Wave equations Particle in a 1D box comparison to hydrogen atom and molecular case 2 Schroedinger equation E V dx d m h = + 2 2 2 2 8 Kinetic energy Potential energy Total energy Timeindependent Schroedinger equation in one dimension (x): = wavefunction Unacceptable wavefunctions: Wellbehaved wavefunction: 1. must be singlevalued at any point 2. must be finite 3. must have a smooth and continuous function 3 Particle in a 1D box Imagine particle in a 1D box with infinite potential barriers: E dx d m h = 2 2 2 2 8 Potential V = 0 in box Total energy is kinetic energy only: What E and are allowed for such an equation? ) cos( ) sin( kx B kx A + = Boundary conditions: ) ( ) ( = = L sin(0) = 0 and cos(0) = 1, if B =0 ) cos( ) sin( ) ( = + = kx B kx A 4 ) sin( kx A = E dx d m h = 2 2 2 2 8 Particle in a 1D box )...
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 Spring '08
 SEABRA
 Physical chemistry, Atom, Mole, pH

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