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Unformatted text preview: Chem120A Notes 9/3/08 1Dimensional Particle in a Box →Particle confined in infinite potential well of length a Schrödinger Equation: ) ( ) ( ) ( ) ( 2 2 x E x x V x m Ψ = Ψ + Ψ ′ ′ →Particle freely moves between 0 and a → < ∞ ≤ ≤ = a x x a x x V ; ) ( → ) ( = Ψ x for < x and a x →continuity of wavefunction requires ) ( = Ψ and ) ( = Ψ a , so that wavefunction is smooth and continuous →these are the boundary conditions →consequences of imposing boundary conditions are quantization and quantum numbers →Inside box, ) ( = x V so the Schrödinger Equation is ) ( ) ( 2 2 x E x m Ψ = Ψ ′ ′ →This is for a x ≤ ≤ , and is similar to what we saw for a free particle ) ( 2 ) ( 2 x mE x Ψ = Ψ ′ ′ → ) ( 2 ) ( 2 = Ψ + Ψ ′ ′ x mE x → ) ( ) ( 2 = Ψ + Ψ ′ ′ x k x (1) Which is similar to a free particle equation where 2 2 2 mE k = (2) (2) can be rearranged to give m k E 2 2 2 = (3) The solutions for (1) are in the form...
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This note was uploaded on 09/28/2009 for the course CHEM 120A taught by Professor Whaley during the Spring '07 term at Berkeley.
 Spring '07
 Whaley
 Physical chemistry, pH

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