Foundations of Quantum Mechanics

University College Dublin

Course Description

  • Course Name

    Foundations of Quantum Mechanics

  • Host University

    University College Dublin

  • Location

    Dublin, Ireland

  • Area of Study

    Mathematics

  • Language Level

    Taught In English

  • Course Level Recommendations

    Upper

    ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

    Hours & Credits

  • ECTS Credits

    5
  • Recommended U.S. Semester Credits
    2.5 - 3
  • Recommended U.S. Quarter Units
    3.75 - 4.5
  • Overview

    This module introduces Quantum Mechanics in its modern mathematical setting. Several canonical, exactly-solvable
    models are studied, including one-dimensional piecewise constant potentials, Dirac potentials, the harmonic
    oscillator, and the Hydrogen atom. Three calculational techniques are introduced: time-independent perturbation
    theory, variational methods, and numerical (spectral) methods. The postulates of Quantum Mechanics,
    [Mathematical background] Complex vector spaces and scalar products, linear forms and duality, the natural scalar product derived from linear forms, Hilbert spaces, linear operators, commutation relations, expectation values, uncertainty, [Time evolution and the Schrodinger equation] Derivation of the Schrodinger equation for time-independent Hamiltonians, the position and momentum representations, the probability current, the free particle [Piecewise constant one-dimensional potentials] Bound and unbound states, wells and barriers, scattering, transmission coefficients, tunneling, [The harmonic oscillator] Solution by power series, Hermite polynomials, creation and annihilation operators, coherent states, [The Hydrogen atom] Solution by separation of variables, quantization of energy and angular momentum, general treatment of central potentials in terms of spherical harmonics, [Angular momentum] Motivation: angular momentum in the hydrogen atom, as derived from spherical harmonics, angular momentum in the abstract setting, intrinsic angular momentum, addition of angular momenta, Clebsch-Gordan coefficients,
    [Approximation methods] Time-independent perturbation theory: the non-degenerate case, variational methods for
    estimating the ground-state energy

Course Disclaimer

Courses and course hours of instruction are subject to change.

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.

ECTS (European Credit Transfer and Accumulation System) credits are converted to semester credits/quarter units differently among U.S. universities. Students should confirm the conversion scale used at their home university when determining credit transfer.

Please reference fall and spring course lists as not all courses are taught during both semesters.

Please note that some courses with locals have recommended prerequisite courses. It is the student's responsibility to consult any recommended prerequisites prior to enrolling in their course.