Next:
Introduction
Up:
Quantum Mechanics I (P303
Previous:
Quantum Mechanics I (P303
Contents
Introduction
The Radiation Laws and the Birth of Quantum Mechanics
Remarks
* Math: Density of states
Waves, particles, and wave packets
Introduction
The wave packet
Interpretation of the Wave Function
Interference experiments
First Axiom
Probability densities
Example: Gauss distribution
Example: distribution
Expectation value (mean value), mean square deviation
The continuity equation
Fourier Transforms and the Solution of the Schrödinger Equation
Math: Fourier Integral
Math: Gauss function
The Delta Functional (`Delta Function')
* Partial Differential Equations and Fourier Transform
Position and Momentum in Quantum Mechanics
Expectation values in quantum mechanics
Example: Wave packet
The commutator
Wave Mechanics
The Stationary Schrödinger Equation
Stationary states
Math Revision: Eigenvalues of a Two-by-Two-Matrix
Stationary States in One Dimension
Piecewise Constant one-Dimensional Potentials
The Infinite Potential Well
Wave functions and eigenenergies
The Hilbert space of wave functions
The Potential Well
Wave functions and energy eigenvalues for
The parity
Even and odd solutions for the potential well
Scattering states in one dimension
Plane waves
Potential scattering
The Tunnel Effect and Scattering Resonances
Potential step
The Tunnel Barrier: Transmission Coefficient
The tunnel barrier: Discussion
A more complicated case
Case of no potential
Tunnel barrier potential within well
The Structure of Quantum Mechanics
Axioms of Quantum Mechanics and the Hilbert Space
Recalling our axioms
Math: The Hilbert Space
Math: Examples of Hilbert spaces
First Axiom: States as Hilbert Space Vectors
Math: Completeness, Dirac notation
Operators and The Two-Level-System I
Operators
Examples for Expectation Values
Matrix Operators and The Two-Level System
Operators and Measurements
Math: Linear Operators
Eigenvalues and Measurement
Example: Position Measurement in the Two-Level system
Energy Measurements
Eigenstates of the Two-Level System
Energy Measurement in the Two-Level System
*Experiments in Double Quantum Dots
Energy Measurement in a Quantum Well
The Two-Level System: Time-Evolution
Time Evolution of States
Important Quantum Mechanical Model Systems
The Harmonic Oscillator I
Model
Solution of the Differential Equation
The Harmonic Oscillator II
The Hilbert space of wave functions
Discussion: Energy Eigenvalues
Harmonic Oscillator: Expectation Values
Ladder Operators, Phonons and Photons
The Ladder Operators and
The Harmonic Oscillator
Phonons and Photons
The Hydrogen Atom
Spherical Symmetric Potentials in 3 Dimensions
The Angular Part
The Radial Part
The Angular Momentum
Definitions
About this document ...
Tobias Brandes 2004-02-04