Quantum Mechanics II
- UE code SPHYB301
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Schedule
45 30Quarter 1
- ECTS Credits 6
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Language
French
- Teacher
Introduction to the Mathematical Concepts of Quantum Mechanics through Postulates
Application of QM in atomic and molecular physics, nuclear physics and solid state physics (including quantum harmonic oscillator)
Kinetic moment and spin
Approximation methods for complex systems
The students will be familiar with the notions of kinetic moment and spin. The applications of QM in atomic and molecular physics, nuclear physics and solid state physics will be addressed : harmonic oscillator, symetries, Hydrogen atoms, approximation methods. These concepts will be preceded by an introduction to the mathematical concepts of quantum mechanics, through its postulates.
The lecture propose an introduction at the use of kinetic moment and spin in quantum mechanics. It addresses also basics problem in physics : harmonic oscillator, symetries, hydrogen atom, approximation methods. These concepts will be preceded by an introduction to the mathematical concepts of quantum mechanics, through its postulates.
Part A
I. Wave-particle duality and quantum measurement
II. Mathematical formulation of the state vector postulate
III. Schrödinger's wave mechanics and Heisenberg's matrix mechanics
IV. Dirac's BRA-KET formalism
Part B
VII. The Harmonic Oscillator in Quantum Physics
1. Harmonic Oscillator Hamiltonian
2. Quantization
3. Creation and Annihilation Operators
4. Expression of the Hamiltonian and Commutation Relations
5. Diagonalization of the Hamiltonian
6. Zero-Point Energy
7. Excitations and Particles
8. States of the Harmonic Oscillator in R Representation
VIII. Angular Momentum in Quantum Physics
1. Angular Momentum
2. The Angular Momentum Operator
3. Magnitude of Angular Momentum
4. Angular Momentum and Central Force
5. Simultaneous Diagonalization of L^2 and L_z
6. Angular Momentum and R Representation
IX. Spin
1. Orbital Magnetic Moment and Angular Momentum
2. Half-Integer Spin Angular Momentum: Stern-Gerlach Experiment
3. Eigenstates and Spin Representation
4. Identical Particles: Bosons and Fermions
5. Spin Precession and Two-Level Systems
Part C
X. Composition of Angular Momenta
XI. Multi-Dimensional Systems
1. Separable Hamiltonian
2. Hamiltonian and Central Potential
3. Hydrogen Atoms
4. Hybrid Orbitals
XII. Stationary Approximation Methods
1. Stationary Perturbation for Non-Degenerate States
2. Stationary Perturbation for Degenerate States
3. Fine Structure of the Hydrogen Atom
XIII. Time-Dependent Approximation Methods
1. Introduction
2. Sinusoidal Perturbation
3. Fermi’s Golden Rule
XIV. Introduction to numerical methods
1. Born-Oppenheimer approximation
2. Independent model
3. Slater determinant
4. One nucleus and several electrons systems
5. Several nuclei and several electrons systems
Use of the blackboard, projections and time for the resoluation of problems (individually and by groups) are alternate
Oral exams with preparation (50 %) during the exam session for theory
Written exams (50%) during the exam session for exercises
If one of the two grades is inferior to 8, the global exam is automatically considered failed (independently of the grade average).
A student that during the first session obtained a mark of a least 10/20 either for the exercises or for the entire theory part benefits from a partial exemption of either the exercises or the entire theory for the second exam session.
During the oral exam, the student will draw two questions, each covering a different part of the course. An insufficient grade on one of the two questions may result in a failure of the entire theory exam.
E. Prugovecki, "Quantum Mechanics in Hilbert space", Dover, 2006.
L. Debnath, P. Mikusinski, "Introduction to Hilbert spaces with applications", Eslevier Academic press, 2005.
C. Cohen-Tannoudji, B. Diu et F. Laloë, Mécanique quantique I (Editions Hermann, Collection : Enseignement des sciences, 1997)
C. Cohen-Tannoudji, B. Diu et F. Laloë, Mécanique quantique II (Editions Hermann, Collection : Enseignement des sciences, 1997)
J.-M. Lévy-Leblond, F. Balibar, Quantique : Rudiments (Dunod, Collection : Les cours de reference, 2007)
C. Ngô, H. Ngô ,Physique quantique : Introduction - Cours et exercices corrigés (Dunod, Collection : Sciences sup physique, 2005)
B.H. Bransden, C.J. Joachain. Quantum Mechanics. Pearson Education (2000)
Mécanique Quantique. C. Aslungul. De Boeck - Larcier (2007)
Quantique. Fondements et applications. J.-P. Pérez, R. Charles, O. Pujol. De Boeck (2013)
Training | Study programme | Block | Credits | Mandatory |
---|---|---|---|---|
Bachelor in Physics | Standard | 0 | 6 | |
Bachelor in Physics | Standard | 3 | 6 |