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Chapter 2 The Particle in a Box

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by

Sungbo Hwang

on 12 December 2012

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Transcript of Chapter 2 The Particle in a Box

Chapter 2
The Particle in a box Differential equation Particle in a
One-Dimensional
box Particle in a Rectangular well Tunneling Differential Equation Ordinary Differential Equation consist of independent variable x and dependent variable y(x) Schrodinger Equation second-order linear homogenous differential equation General Solution Auxiliary Equation Particle in a One-dimensional Box I and III region II region boudary condition , Particle in a One-dimensional Box Quantum Number Kronecker delta orthogonal The Free Particle in one-dimension if E < 0 Energy is not quantize Particle in a rectangular well For Particle in a rectangular well ground-state first excited-state Bound state State satisfied for exist probability for finite region Unbound state State doesn't go to zero as cannot normalize Tunneling Tunneling The penetration of a particle into a classically forbidden region Example Emisson of alpha particle
Inverting of structure of ammonia
Internal rotation of ethane
oxidation-reduction reaction
electrode process
Scanning tunneling microscope Summary Linear, homogeneous, second-order, constant-coefficients differential equation - General Solution - Auxiliary Equation Particle In a One-Dimensional Box - Stationary-state wave function - Energy
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