Unit QUANTUM MECHANICS
- Course
- Physics
- Study-unit Code
- GP005464
- Location
- PERUGIA
- Curriculum
- In all curricula
- Teacher
- Gianluca Grignani
- Teachers
-
- Gianluca Grignani
- Marta Orselli (Codocenza)
- Hours
- 42 ore - Gianluca Grignani
- 42 ore (Codocenza) - Marta Orselli
- CFU
- 12
- Course Regulation
- Coorte 2020
- Offered
- 2022/23
- Learning activities
- Caratterizzante
- Area
- Teorico e dei fondamenti della fisica
- Academic discipline
- FIS/02
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- The crisis of classical physics. Black body theory. Aspects of corpuscular radiation. Atomic models. Heisenberg's uncertainty principle. Wave packet and wave-particle duality. Schroedinger wave mechanics. Eigenvalue equation for Hermitian operators. Pure states. Properties of the discrete spectrum of non-degenerate Hermitian operators. Degenerate discrete spectrum. Continuous spectrum. Mixed spectrum. Unitarity transformations. Time evolution of the mean values ¿¿of physical observables. Stationary states and their properties. One-dimensional problems. Potential well. One-dimensional quantum harmonic oscillator.
Eigenvalue equation for angular momenta.
Three-dimensionlal problems, central potentials, isotropic harmonic oscillator and hydrogenoid atoms.
Time independent and time dependent perturbation theory.
Fine structure of hydrogenoid atoms. Zeeman effect - Reference texts
- author: Cesare Rossetti, title: Rudimenti di Meccanica Quantistica, editor: Levrotto & Bella.
alternatively one can also use the following book: authors: L.D. Landau and E.M. Lifsits, title: Meccanica quantistica, teoria non relativistica, Vol. III, editor: Editori Riuniti. (There is also the english version). - Educational objectives
- The main aim of this teaching is to provide students with the bases needed to address and solve the most important problems in quantum mechanics.
Main knowledge acquired will be:
Knowledge of the solutions of the eigenvalues equations for angular momentum operators.
Knowledge of series solutions of second order differential equations.
Knowledge of the exact solutions of the Schrödinger equation for central potentials as the isotropic harmonic oscillator and the hydrogenoid atom.
Perturbative and variational methods.
Fine structure of hydrogenoid atoms.
The main competence (i. e. the ability to apply the acquired knowledge) will be:
Solutions of the eigenvalue equation for three dimensional Hamiltonians.
Treatment of the eigenvalue problem with central potentials.
Evaluation of the solution of the Schrödinger equation for the hydrogenoid atom. - Prerequisites
- Mathematical Methods for Physicists.
- Teaching methods
- Lectures and exercises
- Other information
- none
- Learning verification modality
- written and oral exam.
- Extended program
- The crisis of classical physics. Black body theory. Aspects of corpuscular radiation. Atomic models. Heisenberg's uncertainty principle. Wave packet and wave-particle duality. Schroedinger wave mechanics. Eigenvalue equation for Hermitian operators. Pure states. Properties of the discrete spectrum of non-degenerate Hermitian operators. Degenerate discrete spectrum. Continuous spectrum. Mixed spectrum. Unitarity transformations. Time evolution of the mean values ¿¿of physical observables. Stationary states and their properties. One-dimensional problems. Potential well. One-dimensional quantum harmonic oscillator.Angular momentum operators Li and their commutators. Eigenvalues and eigenvectors of L^2 and Lz. Derivation of the eigenvalues of J^2 and Jz (for a general angular momentum J¿) with the matrix method: operators J+ and J-.
Three-dimensional problems. Separation of variables in Cartesian and spherical coordiantes. Radial equation and its treatment for a generic potential. Isotropic harmonic oscillator.
Two body problem. Separation of the center of mass motion. Hydrogenoid atoms: energy eigenvalues and eigenfunctions.
Intrinsic angular momentum: spin. Pauli's theory of spin.
Angular momentum composition. Clebsh-Gordan coefficients.
Identical particles and their indistinguibility in a quantum theory. Bosons and Fermions. Pauli exclusion principle. Exclusion principle and periodic table of the elements.
Time independent perturbation theory. Eigenvalues and eigenfunctions at the lowest perturbative order.
An introduction to variational methods.
Time dependent perturbation theory. Transition probability and Fermi's golden rule.
Fine structure of hydrogenoid atoms.
Selection rules.
Semiclassic approximation and W.K.B method.
Zeeman effect.