Syllabus

LEARNING OUTCOMES

After completing the course the student

1. Is familiar with the mathematical structure and postulates of quantum mechanics
2. Can differentiate between the terms quantum-mechanical state and wavefunction
3. Can build a quantum-mechanical Hamiltonian from the classical description of a physical system
4. 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. 
5. Can integrate the quantum evolution and the expectation values of physical quantities for simple systems.
6. Can apply creation and annihilation operators to solve the eigenstates of a one-dimensional harmonic oscillator.
7. Can apply the quantum formalism to model a qubit and a register of several qubits. 
8. Can predict measurent probabilities from a given quantum state.
9. 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:

  Substitutes for Courses

Prerequisites

• valid for whole curriculum period:

  Prerequisites

FURTHER INFORMATION

Further Information

• valid for whole curriculum period:

  Teaching Language: English

  Teaching Period: 2024-2025 Spring V
  2025-2026 Spring V

Description