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Module Specifications..

Current Academic Year 2023 - 2024

Please note that this information is subject to change.

Module Title Quantum Physics II
Module Code PS301
School School of Physical Sciences
Module Co-ordinatorSemester 1: Lampros Nikolopoulos
Semester 2: Lampros Nikolopoulos
Autumn: Lampros Nikolopoulos
Module TeachersLampros Nikolopoulos
NFQ level 8 Credit Rating 5
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None

To introduce the student to introductory topics in quantum mechanics. The formal rules of quantum mechanics are introduced. It is shown how observable quantities such as position, momentum and angular momentum are represented by operators. The properties of these operators are studied. The angular momentum operators are studied in detail leading to a series of applications of the wave equation to 1-, 2- and 3- dimensional physical systems. Emphasis is placed on the central potential and the energy and angular momentum properties of the Hydrogen atom are studied. Simple perturbation methods for solving non-trivial problems are introduced and applications of these methods to atomic and molecular systems are examined.

Learning Outcomes

1. Demonstrate an understanding of how quantum states are described by wave functions;
2. Solve one-dimensional problems involving transmission, reflection and tunnelling of quantum probability amplitudes;
3. Explain the significance of operators and eigenvalue problems in quantum mechanics;
4. Identify and construct the wavefunction for the hydrogen atom and explain the significance of angular momentum operators in atomic physics.
5. Solve the Schrödinger equation and describe the properties of a single particle in one, two and three dimensional potentials
6. Apply first and second order perturbation theory to simple systems

Workload Full-time hours per semester
Type Hours Description
Lecture30No Description
Assignment Completion20No Description
Independent Study75No Description
Total Workload: 125

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Lecture Series: Formulation of QM
Physical states as abstract QM linear vector spaces; Observables as QM operators, Quantum Dynamics, the Schrödinger equation and Measurement. QM principles. Finite and infinite dimension QM systems. Statistical interpretation of QM; Compatible observables and commutators; Heisenberg's uncertainty relations; Eigenstates of an observable as a complete basis set. Superposition principle. Examples in low-dimensional systems (Spin and light polarization); Stern-Gerlach experiment.

Lecture Series: Quantum Dynamics
The Schrödinger equation; connection with Hamilton's classical mechanics formulation; Quantum dynamics with a constant Hamiltonian, (conservation of energy); expansion in an Hamiltonian eigenbasis, the time-evolution operator, Ehrenfest theorem, characteristic time evolution of systems. Examples of low-dimensional systems (e.g. spin and light polarization systems)

Wave mechanics
Wavefunctions as states in a position basis; eigenvalue problem of the position operator; Normalization of improper states, box and delta function normalization. Momentum observable and eigenvalue problem; momentum states; Average and uncertainty of wavefunctions; bound and unbound motion. Particle in 1-D infinite and finite box; wavepacket propagation; momentum eigenstates; proper boundary conditions.

Particle in a harmonic oscillator (HO) potential
The classical HO; the QM formulation of dynamics in a harmonic oscillator potential. The HO eigenvalue problem. Spatial and momentum measurements, uncertainty relations, the Ehrenfest equations of HO-analogy with classical motion.

Spin: a purely QM observable
The concept of Spin; electronic Spin; Stern-Gerlach experiment in more detail; Spin of a composite system; Spin dynamics in constant magnetic fields. Magnetic resonance; two-level systems and Pauli matrices.

Particle in a Coulomb field (hydrogen)
The time-independent Schrödinger equation; Angular momentum observable (conservation of angular momentum); Separation of variables and central-field eigenstates; Spherical harmonics and Laguerre polynomials; Classification of atomic states; Probability distribution; elements of atomic spectroscopy

Learning Activities
Tutorial problems and short projects. Physics: tutorial questions in subjects related with the module's content are worked out; additional questions are provided for homework. Maths: Linear algebra; vector and matrix calculus; eigenvalue matrix problem; ordinary differential equations with constant (and harmonic time-dependent) coefficients; Hermite, Spherical and Laguerre polynomials; delta function and Fourier expansion; spherical coordinate systems.

Assessment Breakdown
Continuous Assessment20% Examination Weight80%
Course Work Breakdown
TypeDescription% of totalAssessment Date
AssignmentTake Home Problem Sets20%Every Second Week
Reassessment Requirement Type
Resit arrangements are explained by the following categories;
1 = A resit is available for all components of the module
2 = No resit is available for 100% continuous assessment module
3 = No resit is available for the continuous assessment component
This module is category 3
Indicative Reading List

  • Robert Scherrer: 0, Quantum Mechanics an Accessible Introduction,
  • A.C.Phillips: 0, Introduction to Quantum Mechanics,
  • R. Harris: 0, NonClassical Physics,
  • J.L. Martin: 0, Basic Quantum Mechanics,
  • A.I.M. Rae: 0, Quantm Mechanics,
  • S. McMurry.: 0, Quantum Mechanics,
  • F. Mandl: 0, Quantum Mechanics,
Other Resources

Programme or List of Programmes
APBSc in Applied Physics
BSSAStudy Abroad (DCU Business School)
BSSAOStudy Abroad (DCU Business School)
HMSAStudy Abroad (Humanities & Soc Science)
HMSAOStudy Abroad (Humanities & Soc Science)
IESAStudy Abroad (Institute of Education)
IESAOStudy Abroad (Institute of Education)
PANBSc Physics with Data Analytics
PBMBSc Physics with Biomedical Sciences
PHABSc in Physics with Astronomy
SHSAStudy Abroad (Science & Health)
SHSAOStudy Abroad (Science & Health)
Date of Last Revision04-SEP-08

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