Introduction to Quantum Theory (videos in Czech)
Intro
Mathematics and Formalism of Quantum Theory (basics)
- Vectors and Scalar Products
- Matrices and Operators
- Eigenvalues and Eigenvectors of Matrices
- Dirac Formalism
- Gram-Schmidt Orthogonalization (11:59) (rovnice: pdf)
- Completness Relation (10:18) (rovnice: pdf)
- Usage of the Completeness Relation (12:22)(equations: above)
- Classical Harmonic Oscillator - part 1 (11:17) (rovnice: pdf)
- Classical Harmonic Oscillator - part 2 (14:47) (equations: above)
- Canonical Quantization (10:48) (rovnice: pdf)
- Model Quantum Mechanics in One Dimension - part 1 (20:26) (rovnice: pdf)
- Model Quantum Mechanics in One Dimension - part 2 (8:44) (equations: above)
- Model Quantum Mechanics in One Dimension - part 3 (10:27) (equations: above)
- Model Quantum Mechanics in One Dimension - part 4 (24:35) (rovnice: pdf)
General Comments
- Two-Level Systems in General (15:35) (rovnice: pdf)
- Comment on (Ir)reversibility and Energy Conservation (18:18) (rovnice: pdf)
- Energy of a Two-Level System (9:51) (rovnice: pdf)
- Momentum Operator in Two-Level System (9:18) (equations: above)
- Limits of Population Oscillations in a Two-Level System (9:10) (equations: above)
Historical Notes
- Werner Heisenberg, Zeitschrift für Physik 33 (1925) 879
- Introduction of Operators into Quantum Mechanics - part 1 (18:22) (rovnice: pdf)
- Introduction of Operators - part 2 - Anharmonic oscillator - 1 (11:42) (equations: above)
- Introduction of Operators - part 3 - Anharmonic oscillator - 2 (17:43) (rovnice: pdf)
- Introduction of Operators - part 4 - ... Matrices at last (27:49) (rovnice: pdf)
- Introduction of Operators - part 5 - Sommerfeld Quantization Conditions (12:38) (rovnice: pdf)
- Introduction of Operators - part 6 - More about Quantization Conditions (13:39)(equations: above)
- Introduction of Operators - part 7 - Canonical Commutation Relations (11:25)(equations: above)
- Paul Adrien Maurice Dirac, Proc. R. Soc. Lond. A 109 (1925) 642–653 (open access)
- Meaning of the Commutator
Two Level Systems and QBits
Time Evolution in Quantum Theory
- Schrödinger Equation and Evolution Operator
- Two-Level System
- Interacting Two-Level Systems - part 1 (23:24) (rovnice: pdf)
- Interacting Two-Level Systems - part 2 (28:41) (rovnice: pdf)
Time-Dependent Interaction and External Driving
- Role of Resonance in Two-level Transitions - part 1 (7:07) (rovnice: pdf)
- Role of Resonance in Two-level Transitions - part 2 (14:45) (equations: above)
- Role of Resonance in Two-level Transitions - part 3 (19:36) (rovnice: pdf)
- Role of Resonance in Two-level Transitions (part 4) (16:42) (rovnice: pdf)
- Role of Resonance in Two-level Transitions - Appendix (20:06) (rovnice: pdf)
- Photon Echo part 1 (10:11) (rovnice: pdf)
- Photon Echo (part 2) (16:02) (equations: above)
- Evolution Operator for Time-Dependent Hamiltonian (15:34) (rovnice: pdf)
- Excitation by a Delta Pulse (part 1) (12:28) (rovnice: pdf)
- Excitation by a Delta Pulse (part 2) (16:18) (equations: above)
- Excitation by a Delta Pulse (part 3) (12:18) (equations: above)
- Excitation by a Delta Pulse and Example of Entanglement Formation between Two Systems (24:41) (rovnice: pdf)
Formalism for Systems with Many Degrees of Freedom
- Formalism for Many Systems and Intro to QBit Gates (28:19) (rovnice: pdf)
- Operations on Two QBits and the Measurement Problem (17:59) (rovnice: pdf)
- Games with QBits and Quantum State Teleportation (part 1) (11:08) (rovnice: pdf)
- Games with QBits and Quantum State Teleportation (part 2) (17:51) (equations: above)
- No-Cloning Theorem (17:02) (rovnice: pdf)
Harmonic Oscillator
Harmonic Oscillator Eigenvalues and Eigenvectors
- Quantum Harmonic Oscillator - part 1 (11:16) (rovnice: pdf)
- Quantum Harmonic Oscillator - part 2 (10:58) (equations: above)
- Quantum Harmonic Oscillator - part 3 (12:23) (equations: above)
- Quantum Harmonic Oscillator - part 4 (15:07) (rovnice: pdf)
- Quantum Harmonic Oscillator - part 5 (13:15) (rovnice: pdf)
- Dipole Transitions in Harmonic Oscillator - part 1 (10:22) (rovnice: pdf)
- Dipole Transitions in Harmonic Oscillator - part 2 (15:28) (equations: above)
Harmonic Oscillator in Coordinate Representation
- Harmonic Oscillator in Coordinate Representation - part 1 (15:53) (rovnice: pdf)
- Harmonic Oscillator in Coordinate Representation - part 2 (20:29) (rovnice: pdf)
- Initial Conditions for the Motion of Harmonic Oscillator (10:11) (rovnice: pdf)
- Shifted Ground-State of Harmonic Oscillator (10:34) (equations: above)
- Time-Evolution of Coherent State (13:19) (rovnice: pdf)
- Time-Dependent Shift Operator (11:18) (equations: above)
- Shape and Position of the Wavepacket (14:52) (equations: above)
Approximative Methods in Quantum Mechanics
Variational Principle
- Ritz Variational Principle (25:39) (rovnice: pdf)
- Ground State of Hydrogen Atom (23:28) (rovnice: pdf)
Perturbation Theory
- Introduction to Perturbation Theory (11:46) (rovnice: pdf)
- Corrections of the First Order (9:09)(equations: above)
- Corrections of the Second Order (11:27) (rovnice: pdf)
Further Model Systems
Angular Momentum
- Operator of Angular Momentum (16:16) (rovnice: pdf)
- Commutation Relations of the Angular Momentum Operator (16:55) (equations: above)
Potential Well
- Infinitely Deep Rectangular Potential Well (8:17) (rovnice: pdf)
- *Unsuccessful Solution by Fourier Series (25:10)(equations: above)
- Standard Solution of the Potential Well (14:39) (rovnice: pdf)
- Selection Rules of an Even Potential (15:45)(equations: above: above)
- *Ground State in the Form of a Fourier Series (14:57) (rovnice: pdf)
- *Infinitely Deep Potential Well as a Generalised Eigenproblem (13:39) (rovnice: pdf)
- *Outline of the Solution by Basis Orthogonalization (10:30)(equations: above)
- Rectangular Well with Finite Depth - part 1 (18:08) (rovnice: pdf)
- Rectangular Well with Finite Depth - part 2 (20:13)(equations: above)
Rigid Rotator
- Rigid rotator - part 1 (15:09) (rovnice: pdf)
- Rigid Rotator - part 2 (10:03) (rovnice: pdf)
- Rigid Rotator - part 3 (13:26)(equations: above)
- Rigid Rotator - part 4 (17:15) (rovnice: pdf)
- Eigenfunctions in Spherical Coordinate Theta (20:56) (rovnice: pdf)
Laplacian in Spherical Coordinates
- *Nabla with Components Expressed in Spherical Coordinates - part 1 (17:37) (rovnice: pdf)
- *Nabla with Components Expressed in Spherical Coordinates - part 2 (14:41)(equations: above)
- *Nabla in Spherical Coordinates - part 1 (11:52) (rovnice: pdf)
- *Nabla in Spherical Coordinates - part 2 (7:35)(equations: above)
- *Laplace Operator in Spherical Coordinates (derivation one) - part 1 (15:22) (rovnice: pdf)
- *Laplace Operator in Spherical Coordinates (derivation one) - part 2 (25:52) (rovnice: pdf)
- *Laplace Operator in Spherical Coordinates (derivation two) - part 1 (13:56) (rovnice: pdf)
- *Laplace Operator in Spherical Coordinates (derivation two) - part 2 (17:49)(equations: above)
Hydrogen Atom
Introduction to the Problem
- Two-body Problem (20:33) (rovnice: pdf)
- Atomic Units (11:22) (rovnice: pdf)
- Angular Momentum in Spherical Coordinates (13:57) (rovnice: pdf)
- Separation of Variables (8:23) (rovnice: pdf)
s-states of the Hydrogen Atom
- Transformation into a Problem with Discrete Only Spectrum
- ... in preparation