Quantum Phisycs 2
A.Y. 2019/2020
Learning objectives
This is an advanced quantum mechanics course which, bulding upon
the previous introductory course (first semester) discussed
three-dimensional systems (in particular the hydrogen atoms) and a
variety of theoretical devolpments, including the theory of angular
momentum and spin, path-integral methods, perturbation and scattering
theory, identical particles and entanglement
the previous introductory course (first semester) discussed
three-dimensional systems (in particular the hydrogen atoms) and a
variety of theoretical devolpments, including the theory of angular
momentum and spin, path-integral methods, perturbation and scattering
theory, identical particles and entanglement
Expected learning outcomes
At the end of these courses the student
1. will be able to treat the Schrödinger equation for systems of two particles (even identical) interacting through a potential
2. will be able to determine the spectrum of the Hamiltonian for central problems by using spherical coordinates
3. will be able to determine the spectrum of the hydrogen atom
4. will be able to determine the spectrum of angular momentum operators orbital and intrinsic (spin) and will know how to compose angular moments
5. will be able to relate the laws of motion of classical mechanics to those of the quantum mechanics, both using the WKB method, and using the path integral method
6. will know how to calculate the time-independent perturbation to the spectrum of a known Hamiltonian
7. will be able to determine a transition amplitude using time-dependent perturbation theory
8. will be able to express the cross section in terms of a transitional range
9. will be able to write the wave function for a system of identical particles
10. will be able to determine the density matrix for a given statistical mixture and use it to calculate an average value
1. will be able to treat the Schrödinger equation for systems of two particles (even identical) interacting through a potential
2. will be able to determine the spectrum of the Hamiltonian for central problems by using spherical coordinates
3. will be able to determine the spectrum of the hydrogen atom
4. will be able to determine the spectrum of angular momentum operators orbital and intrinsic (spin) and will know how to compose angular moments
5. will be able to relate the laws of motion of classical mechanics to those of the quantum mechanics, both using the WKB method, and using the path integral method
6. will know how to calculate the time-independent perturbation to the spectrum of a known Hamiltonian
7. will be able to determine a transition amplitude using time-dependent perturbation theory
8. will be able to express the cross section in terms of a transitional range
9. will be able to write the wave function for a system of identical particles
10. will be able to determine the density matrix for a given statistical mixture and use it to calculate an average value
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
CORSO A
Lesson period
First semester
Course syllabus
--Introduction to the theory of groups
+Rotation group and its representation
--Quantum mechanics in more than one dimension +Direct product spaces
+Separable potentials
+The two-bosy problem and central problems --Angular momentum
+Elements of group theory
+Rotations and angular momentum
+The angular momentum operator and its spectrum
+Spin
+Addition of angular momenta
--Three-dimensional problems
+The radial Schroedinger equation
+The isotropic harmonic oscillator
+The Coulomb potential and the hydrogen atom
--The classical limit of quantum mechanics
+The action in quantum mechanics
+Lagrangean quantum mechaincs andf the path-integral approach
+The semiclassical (WKB) approximation
--Perturbation theory
+Time-independent perturbation theory
+Time-dependent perturbation theory and the interaction picture
--Identical particles
+Many-particle systems
+Bose and Fermi statistics
+The spin-statistics theorem
--Entanglement
+Quantum statistical mechanics and density matrix
+Rotation group and its representation
--Quantum mechanics in more than one dimension +Direct product spaces
+Separable potentials
+The two-bosy problem and central problems --Angular momentum
+Elements of group theory
+Rotations and angular momentum
+The angular momentum operator and its spectrum
+Spin
+Addition of angular momenta
--Three-dimensional problems
+The radial Schroedinger equation
+The isotropic harmonic oscillator
+The Coulomb potential and the hydrogen atom
--The classical limit of quantum mechanics
+The action in quantum mechanics
+Lagrangean quantum mechaincs andf the path-integral approach
+The semiclassical (WKB) approximation
--Perturbation theory
+Time-independent perturbation theory
+Time-dependent perturbation theory and the interaction picture
--Identical particles
+Many-particle systems
+Bose and Fermi statistics
+The spin-statistics theorem
--Entanglement
+Quantum statistical mechanics and density matrix
Prerequisites for admission
Non-relativistic quantum mechanics in one dimension. Basic knowledge of classical mechanics and analytical mechanics, mathematical analysis, geometry and linear algebra.
Teaching methods
The teaching method consists of theory lessons on the blackboard and in the performance of exercises and applications of the topics covered.
Teaching Resources
Textbooks:
J.J. Sakurai, Modern Quantum Mechanics, Cambridge UP;
S. Forte, L. Rottoli, Fisica quantistica, Zanichelli;
L.D. Landau, E.M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, Elsevier; R.P. Feynman et al., The Feynman Lectures on Physics III, Addison-Wesley Pub.; P.A.M. Dirac, The Principles Of Quantum Mechanics, Oxford Science Publications; S. Patri', M. Testa, Fondamenti di Meccanica Quantistica, Ed. Nuova Cultura;
L.E. Picasso, Lectures In Quantum Mechanics, Springer;
Collections of solved exercises:
G. Passatore, Problemi di meccanica quantistica elementare, Franco Angeli;
L. Angelini, Meccanica quantistica: problemi scelti, Springer;
E. d'Emilio, L. E. Picasso, Problems in Quantum Mechanics, Springer;
A. Z. Capri, Promlems and Solutions in Nonrelativistic Quantum Mechanics, World Scientific; K. Tamvakis, Problems and Solutions in Quantum Mechanics, Cambridge U.P.;
V. Galitski, B. Karnakov, V. Kogan e V. Galitski, Exploring Quantum Mechanics, Oxford U.P.;
J.J. Sakurai, Modern Quantum Mechanics, Cambridge UP;
S. Forte, L. Rottoli, Fisica quantistica, Zanichelli;
L.D. Landau, E.M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, Elsevier; R.P. Feynman et al., The Feynman Lectures on Physics III, Addison-Wesley Pub.; P.A.M. Dirac, The Principles Of Quantum Mechanics, Oxford Science Publications; S. Patri', M. Testa, Fondamenti di Meccanica Quantistica, Ed. Nuova Cultura;
L.E. Picasso, Lectures In Quantum Mechanics, Springer;
Collections of solved exercises:
G. Passatore, Problemi di meccanica quantistica elementare, Franco Angeli;
L. Angelini, Meccanica quantistica: problemi scelti, Springer;
E. d'Emilio, L. E. Picasso, Problems in Quantum Mechanics, Springer;
A. Z. Capri, Promlems and Solutions in Nonrelativistic Quantum Mechanics, World Scientific; K. Tamvakis, Problems and Solutions in Quantum Mechanics, Cambridge U.P.;
V. Galitski, B. Karnakov, V. Kogan e V. Galitski, Exploring Quantum Mechanics, Oxford U.P.;
Assessment methods and Criteria
The exam consists of a written test, which contributes together with the test of module 1 to the determination of the final vote. Alternatively an overall written test of both modules.
The exam will evaluate both the skills acquired and the ability to solve new problems.
The exam will evaluate both the skills acquired and the ability to solve new problems.
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 8
Practicals: 30 hours
Lessons: 40 hours
Lessons: 40 hours
Professor:
Caracciolo Sergio
Shifts:
-
Professor:
Caracciolo SergioCORSO B
Responsible
Lesson period
First semester
Course syllabus
--Quantum mechanics in more than one dimension
+Direct product spaces
+Separable potentials
+The two-bosy problem and central problems
--Angular momentum
+Elements of group theory
+Rotations and angular momentum
+The angular momentum operator and its spectrum
+Spin
+Addition of angular momenta
--Three-dimensional problems
+The radial Schroedinger equation
+The isotropic harmonic oscillator
+The Coulomb potential and the hydrogen atom
--The classical limit of quantum mechanics
+The action in quantum mechanics
+Lagrangean quantum mechaincs andf the path-integral approach
+The semiclassical (WKB) approximation
--Perturbation theory
+Time-independent perturbation theory
+Time-dependent perturbation theory and the interaction picture
+Introduction to scattering theory
--Identical particles
+Many-particle systems
+Bose and Fermi statistics
+The spin-statistics theorem
--Entanglement
+Quantum statistical mechanics and density matrix
+The Einstein-Podolsky-Rosen paradox and local realism
+Bell inequalities, the measurement problem and e paradoxes of quantum mechanics
+Direct product spaces
+Separable potentials
+The two-bosy problem and central problems
--Angular momentum
+Elements of group theory
+Rotations and angular momentum
+The angular momentum operator and its spectrum
+Spin
+Addition of angular momenta
--Three-dimensional problems
+The radial Schroedinger equation
+The isotropic harmonic oscillator
+The Coulomb potential and the hydrogen atom
--The classical limit of quantum mechanics
+The action in quantum mechanics
+Lagrangean quantum mechaincs andf the path-integral approach
+The semiclassical (WKB) approximation
--Perturbation theory
+Time-independent perturbation theory
+Time-dependent perturbation theory and the interaction picture
+Introduction to scattering theory
--Identical particles
+Many-particle systems
+Bose and Fermi statistics
+The spin-statistics theorem
--Entanglement
+Quantum statistical mechanics and density matrix
+The Einstein-Podolsky-Rosen paradox and local realism
+Bell inequalities, the measurement problem and e paradoxes of quantum mechanics
Prerequisites for admission
Non-relativistic quantum mechanics in one dimension. Basic knowledge of classical mechanics and analytical mechanics, mathematical analysis, geometry and linear algebra.
Teaching methods
The teaching method consists of theory lessons on the blackboard and in the solution of exercises and applications on the topics covered.
Teaching Resources
Textbooks:
J.J. Sakurai, Modern Quantum Mechanics, Cambridge UP;
S. Forte, L. Rottoli, Fisica quantistica, Zanichelli;
L.D. Landau, E.M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, Elsevier;
R.P. Feynman et al., The Feynman Lectures on Physics III, Addison-Wesley Pub.;
P.A.M. Dirac, The Principles Of Quantum Mechanics, Oxford Science Publications;
S. Patri', M. Testa, Fondamenti di Meccanica Quantistica, Ed. Nuova Cultura;
L.E. Picasso, Lectures In Quantum Mechanics, Springer;
Collections of solved exercises:
G. Passatore, Problemi di meccanica quantistica elementare, Franco Angeli;
L. Angelini, Meccanica quantistica: problemi scelti, Springer;
E. d'Emilio, L. E. Picasso, Problems in Quantum Mechanics, Springer;
A. Z. Capri, Promlems and Solutions in Nonrelativistic Quantum Mechanics, World Scientific;
K. Tamvakis, Problems and Solutions in Quantum Mechanics, Cambridge U.P.;
V. Galitski, B. Karnakov, V. Kogan e V. Galitski, Exploring Quantum Mechanics, Oxford U.P.;
J.J. Sakurai, Modern Quantum Mechanics, Cambridge UP;
S. Forte, L. Rottoli, Fisica quantistica, Zanichelli;
L.D. Landau, E.M. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, Elsevier;
R.P. Feynman et al., The Feynman Lectures on Physics III, Addison-Wesley Pub.;
P.A.M. Dirac, The Principles Of Quantum Mechanics, Oxford Science Publications;
S. Patri', M. Testa, Fondamenti di Meccanica Quantistica, Ed. Nuova Cultura;
L.E. Picasso, Lectures In Quantum Mechanics, Springer;
Collections of solved exercises:
G. Passatore, Problemi di meccanica quantistica elementare, Franco Angeli;
L. Angelini, Meccanica quantistica: problemi scelti, Springer;
E. d'Emilio, L. E. Picasso, Problems in Quantum Mechanics, Springer;
A. Z. Capri, Promlems and Solutions in Nonrelativistic Quantum Mechanics, World Scientific;
K. Tamvakis, Problems and Solutions in Quantum Mechanics, Cambridge U.P.;
V. Galitski, B. Karnakov, V. Kogan e V. Galitski, Exploring Quantum Mechanics, Oxford U.P.;
Assessment methods and Criteria
The exam consists of a written test, which contributes together with the test of module 1 to the determination of the final vote. Alternatively an overall written test of both modules.
The exam will evaluate both the skills acquired and the ability to solve new problems.
The exam will evaluate both the skills acquired and the ability to solve new problems.
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 8
Practicals: 30 hours
Lessons: 40 hours
Lessons: 40 hours
Professor:
Ferrera Giancarlo
Shifts:
-
Professor:
Ferrera GiancarloProfessor(s)