THREE-DIMENSIONAL MODELING

Course objectives

GENERAL OBJECTIVES: The course aims at introducing the basic notions of nonrelativistic quantum mechanics and of statistical mechanics and illustrating their application to symple physical systems. At the end of the course, students will possess the fundamentals of both theories. They will have also acquired the skills necessary to solve Schrodinger’s equation and evaluate the partition function of simple systems of noninteracting particles obtaining the corresponding physical properties. SPECIFIC OBJECTIVES: A - Knowledge and understanding OF 1) To know the basic notions of nonrelativistic quantum mechanics for a single particle or a system of noninteracting particles. OF 2) To understand the notion of spin and the composition of angular momenta. OF 3) To know the perturbation theory, time dependent and time independent, also in the presence of degeneracy. OF 4) To understand the connection between particle spin and particle exchange symmetry for a quantum state. OF 5) To know the basic notions of statistical mechanics for systems of noninteracting particles, classical or quantum. OF 6) To understand the notions of micro- and macrostate as well as that of equilibrium state in the case of microcanonical, canonical and grancanonical ensembles. OF 7) To know the main state functions and their relations B - Application skills OF 8) To be able to face with conceptual problems among the arguments discussed. OF 9) To be able to solve simple problems with analytical techniques. OF 10) To be able to lay out a problem to be solved with numerical techniques. C - Autonomy of judgment OF 11) To be able to establish a bidirectional link between mathematical solutions of a problem and the physical properties of the corresponding system. D - Communication skills OF 12) To be able to communicate in a synthetic but comprehensive way the solution of problems and its logical structure. E - Ability to learn OF 13) Have the ability to consult different textbooks using different notations.

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BERNARD VAN HECK Lecturers' profile

Program - Frequency - Exams

Course program
The crisis of classical physics Mathematical structure of quantum mechanics Schrödinger equation Quantum mechanics in 1D: bound states, scattering, harmonic oscillator Symmetries in quantum mechanics Theory of angular momentum The hydrogen atom Time-independent perturbation theory Identical particles
Prerequisites
Math: complex analysis, linear algebra, probability Physics: classical mechanics and electromagnetism
Books
R. Shankar, Principles of Quantum Mechanics, 2nd edition. J.J. Sakurai e J. Napolitano, Modern Quantum Mechanics, 3rd edition, Cambridge
Frequency
Optional
Exam mode
The exam consists of a written test and an oral one . Passing the written test is a prerequisite for admission to the oral test. The final grade is the result of an overall evaluation of the written test and the oral test. The written exam consists of 3-4 exercises to be solved in 3 hours. The minimum passing grade is 18/30. During the written exam it is possible to consult textbooks and course notes, but not tablets or collections of solved exercises. The written grade is valid for one exam session (winter / summer / autumn). If, after the oral exam, the final grade is insufficient or rejected by the student, the grade of the written exam will be lost. It is possible to attempt the written test in consecutive sessions belonging to the same session. For the purposes of the final grade, only the last written exam handed in is valid.
Bibliography
D.J. Griffiths, Introduction to Quantum Mechanics, 2nd edition, Pearson Prentice Hall. L.D. Landau e E.M. Lifhsitz, Quantum Mechanics: Non-Relativistic Theory (Course of Theoretical Physics: Volume 3), Butterworth-Heinemann J.J. Sakurai e J. Napolitano, Modern Quantum Mechanics (third edition), Cambridge University Press R. Shankar, Principles of Quantum Mechanics (second edition), Springer L. Picasso, Lezioni di Meccanica Quantistica (seconda edizione), edizioni ETS D. Tong, Lectures on Quantum Mechanics, available online. S. Weinberg, Lectures on Quantum Mechanics (seconda edizione), Cambridge Univ. Press
BERNARD VAN HECK Lecturers' profile

Program - Frequency - Exams

Course program
The crisis of classical physics Mathematical structure of quantum mechanics Schrödinger equation Quantum mechanics in 1D: bound states, scattering, harmonic oscillator Symmetries in quantum mechanics Theory of angular momentum The hydrogen atom Time-independent perturbation theory Identical particles
Prerequisites
Math: complex analysis, linear algebra, probability Physics: classical mechanics and electromagnetism
Books
R. Shankar, Principles of Quantum Mechanics, 2nd edition. J.J. Sakurai e J. Napolitano, Modern Quantum Mechanics, 3rd edition, Cambridge
Frequency
Optional
Exam mode
The exam consists of a written test and an oral one . Passing the written test is a prerequisite for admission to the oral test. The final grade is the result of an overall evaluation of the written test and the oral test. The written exam consists of 3-4 exercises to be solved in 3 hours. The minimum passing grade is 18/30. During the written exam it is possible to consult textbooks and course notes, but not tablets or collections of solved exercises. The written grade is valid for one exam session (winter / summer / autumn). If, after the oral exam, the final grade is insufficient or rejected by the student, the grade of the written exam will be lost. It is possible to attempt the written test in consecutive sessions belonging to the same session. For the purposes of the final grade, only the last written exam handed in is valid.
Bibliography
D.J. Griffiths, Introduction to Quantum Mechanics, 2nd edition, Pearson Prentice Hall. L.D. Landau e E.M. Lifhsitz, Quantum Mechanics: Non-Relativistic Theory (Course of Theoretical Physics: Volume 3), Butterworth-Heinemann J.J. Sakurai e J. Napolitano, Modern Quantum Mechanics (third edition), Cambridge University Press R. Shankar, Principles of Quantum Mechanics (second edition), Springer L. Picasso, Lezioni di Meccanica Quantistica (seconda edizione), edizioni ETS D. Tong, Lectures on Quantum Mechanics, available online. S. Weinberg, Lectures on Quantum Mechanics (seconda edizione), Cambridge Univ. Press
  • Academic year2025/2026
  • CoursePhysics
  • CurriculumFisica applicata
  • Year3rd year
  • Semester1st semester
  • SSDFIS/02
  • CFU6