LEARNING OUTCOMES
After completing the course the student
- Is familiar with the mathematical structure and postulates of quantum mechanics
- Can differentiate between the terms quantum-mechanical state and wavefunction
- Can build a quantum-mechanical Hamiltonian from the classical description of a physical system
- Can solve the eigenstates and eigenvalues of the Schrödinger equation in simple situations and knows how to generalize the computation to situations where analytical solution is challenging.
- Can integrate the quantum evolution and the expectation values of physical quantities for simple systems.
- Can apply creation and annihilation operators to solve the eigenstates of a one-dimensional harmonic oscillator.
- Can apply the quantum formalism to model a qubit and a register of several qubits.
- Can predict measurent probabilities from a given quantum state.
- Can apply perturbation theory to compute eigensolutions in a situation where analytical solutions is challenging.
Credits: 5
Schedule: 14.04.2025 - 02.06.2025
Teacher in charge (valid for whole curriculum period):
Teacher in charge (applies in this implementation): Jani-Petri Martikainen
Contact information for the course (applies in this implementation):
CEFR level (valid for whole curriculum period):
Language of instruction and studies (applies in this implementation):
Teaching language: English. Languages of study attainment: English
CONTENT, ASSESSMENT AND WORKLOAD
Content
valid for whole curriculum period:
Hilbert space and Dirac notation; Bases and operators; Properties of (Hermitian) operators; Eigenvalues and eigenfunctions; Postulates of quantum mechanics including quantum measurement; Expectation values and variance; Uncertainty relations; Continuous-variable bases: coordinate representation, momentum basis; Quantization recipe for physical systems; Schrödinger equation and unitary temporal evolution; Qubit (two-level system); Bipartite system and entanglement; Quantum gates and algorithms; Commutator and conserved quantities; Solving 1D harmonic oscillator using creation and annihilation operators; Excited states of a 1D harmonic oscillator; Free particles and plane waves; Particle in different 1D potentials: box, square well, constant potential with periodic boundary conditions; Scattering and tunneling through barriers; Time-independent perturbation theory; Temporal dependence of operators; Different pictures of quntum mechanics; Rabi oscillations
Assessment Methods and Criteria
valid for whole curriculum period:
Teaching methods: lectures and exercises
Assessment methods: exam, to which one obtains bonus points by solving the exercises according to rules agreeded in the beginning of the course.
Workload
valid for whole curriculum period:
Lectures, exercises, exam, and independent work.
DETAILS
Study Material
valid for whole curriculum period:
This course has its own extensive lecture notes written in LaTeX which work as the main study material. For additional materials, some students may find the following textbooks useful: R. L. Liboff: Introductory Quantum Mechanics, Ballentine: Quantum Mechanics - A Modern Development, Griffiths: Introduction to Quantum mechanics, Bolton & Lambourne: The Quantum World: wave mechanics.
Substitutes for Courses
valid for whole curriculum period:
Prerequisites
valid for whole curriculum period:
FURTHER INFORMATION
Further Information
valid for whole curriculum period:
Teaching Language: English
Teaching Period: 2024-2025 Spring V
2025-2026 Spring V