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Contents
Contents
UMIST, 2004
Course homepage: http://brandes.phy.umist.ac.uk/QM/
Quantum Mechanics I (Example Sheets)
Dr. Tobias Brandes
Contents
The Radiation Laws and the Birth of Quantum Mechanics
Kirchhoff (5 min)
Rayleigh-Jeans law (5 min)
* Planck's law (10 min)
** Stefan-Boltzmann constant (20-60 min)
Waves, particles, and wave packets
Macroscopic Object (5 min)
* Geometrical Optic (2 min)
Interpretation of the Wave Function
Schrödinger Equation (5 min)
Interpretation of the Wave Function (2 min)
Probability (2 min)
Probability and current density of a particle (15 min)
Fourier Transforms and the Solution of the Schrödinger Equation
Definition of the Fourier Integral (2 min)
** Math: Gauß (20 min)
* Math: Gauß Integral 1 (10 min)
Math: Gauß Integral 2 (10 min)
Math: Fourier Transform of Gauss Function (20 min)
* Wave packet (20 min)
Position and Momentum in Quantum Mechanics
Normalization (2min)
Expectation values in quantum mechanics (5min)
Wave packet (10-30 min)
* Hamilton function (10min)
* Commutator 1 (10 min)
The stationary Schrödinger Equation
Definitions (2min)
Piecewise constant potentials in one dimension (5min)
The Infinite Potential Well
Energies and Eigenstates I (10-20 min)
Energies and Eigenstates II (10-20 min)
* Orthonormality (10 min)
Time Evolution (2 min)
Expectation values (15 min)
* Time evolution of superposition (10 min)
The Finite Potential Well
Parity (10 min)
Wave functions (5 min)
Scattering states in one dimension
Plane Waves (5 min)
Piecewise constant potential (25 min)
Transfer matrix (5 min)
Transmission, * Reflection (10min)
The Tunnel Effect and Scattering Resonances
-matrix for tunnel barrier (15 min)
* Transmission coefficient (15 min)
Transmission coefficient (10 min)
** Determinant of
(10 min)
** A more general definition of the transfer matrix
(
min)
Axioms of Quantum Mechanics and the Hilbert Space
Definition (2min)
Orthonormality (5 min)
* Expansion into eigenmodes (40 min)
* Scalar product (20 min)
Operators and Measurements in Quantum Mechanics
Definitions (2 min)
Adjoint operator (10 min)
Observables (5 min)
Eigenvalues (5min)
The Two-Level System I
Model (20 min)
Eigenvalues of the energy, eigenvectors (50 min)
Absorption Experiment (5 min)
* Vector Representation (10 min)
The Two-Level System: Measurements and Probabilities
Qubit 1 (5 min)
Qubit 2 (5 min)
Qubit 3: NOT-Gate (5 min)
* Qubit 4: HADAMARD-Gate (10 min)
The Harmonic Oscillator
Model (2 min)
Energies (2 min)
Linear combination (10-20 min)
** Generating Function (5-30 min)
Ladder Operators and Phonons
Commutator (5 min)
Hamiltonian (10 min)
Ladder Operator (5 min)
Ladder Operator (15 min)
Ground state (20 min)
Central Potentials in Three Dimensions
Separations of Variables (20 min)
* Behavior for
und
(10-20 min)
About this document ...
Tobias Brandes 2004-02-04
-matrix for tunnel barrier (15 min)
(10 min)
(
min)
und
(10-20 min)