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Probability theory
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Outline of course
Contents
Fundamentals
Subsections
Probability theory
Introduction
What is probability?
Combining probabilities
The mean, variance, and standard deviation
Continuous probability distributions
Problems
Wave-particle duality
Introduction
Classical light-waves
The photoelectric effect
Quantum theory of light
Classical interference of light-waves
Quantum interference of light
Classical particles
Quantum particles
Wave-packets
Evolution of wave-packets
Heisenberg's uncertainty principle
Schrödinger's equation
Collapse of the wave-function
Problems
Fundamentals of quantum mechanics
Introduction
Schrödinger's equation
Normalization of the wave-function
Expectation values and variances
Ehrenfest's theorem
Operators
The momentum representation
The uncertainty principle
Eigenstates and eigenvalues
Measurement
Continuous eigenvalues
Stationary states
Problems
One-dimensional potentials
Introduction
The infinite potential well
The square potential barrier
The WKB approximation
Cold emission
-decay
The square potential well
The simple harmonic oscillator
Problems
Multi-particle systems
Introduction
Fundamental concepts
Non-interacting particles
Two-particle systems
Identical particles
Problems (N.B. Neglect spin in the following questions.)
Three-dimensional quantum mechanics
Introduction
Fundamental concepts
Particle in a box
Degenerate electron gases
White-dwarf stars
Problems
Orbital angular momentum
Introduction
Angular momentum operators
Representation of angular momentum
Eigenstates of angular momentum
Eigenvalues of
Eigenvalues of
Spherical harmonics
Problems
Central potentials
Introduction
Derivation of radial equation
The infinite potential well
The hydrogen atom
The Rydberg formula
Problems
Spin angular momentum
Introduction
Spin operators
Spin space
Eigenstates of
and
The Pauli representation
Spin precession
Problems
Addition of angular momentum
Introduction
General principles
Angular momentum in the hydrogen atom
Two spin one-half particles
Problems
Richard Fitzpatrick 2006-12-12
-decay
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