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Lecture Outline 3

# Lecture Outline 3 - CHEM 332 Physical Chemistry II Lecture...

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CHEM 332 Physical Chemistry II Lecture Outline 11 February 2014 Particle in a One Dimensional Box and a Three Dimensional Box VIII. Particle in a One Dimensional Box with a Finite Wall Write the Classical Hamiltonian where V = Region I 0 Region II U Region III Write the Hamiltonian Operator Solve the Schrodinger Wave Equation Region I = 0 Region II After Applying the Boundary Condition = 0 at x = 0

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Region III Case for (E - U) < 0: Boundary Condition II = III at x = L Boundary Condition d II /dx = d III /dx at x = L Solving the Above Two Equations Simultaneously for the Energy E Gives: Lowe Provides Graphs of the Left-Hand Side and Right-Side of This Equation for Specific Values of m, L and U . The Energy is Given by the Intersection of These Graphs.
Notice: (i) The Solution for E is Quantized. (Bound System) (ii) The Energies for the Lowest Lying States are Slightly Lower than Would be Expected if the "Wall" at L were Infinite. (The Particle Behaves as though It is In a Larger Box.) Lowe Provides Graphs of

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