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 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. 
4. Can integrate the quantum evolution and the expectation values of physical quantities for simple systems.
5. Can apply creation and annihilation operators to solve the eigenstates of a one-dimensional harmonic oscillator.
6. Can apply the quantum formalism to model a qubit and a register of several qubits. 
7. Can predict measurent probabilities from a given quantum state.
8. Can apply perturbation theory to compute eigensolutions in a situation where analytical solutions is challenging. 

Credits: 5

Schedule: 24.10.2022 - 07.12.2022

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Tapio Ala-Nissilä, Mikko Möttönen

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; Operators, eigenvalues and eigenfunctions; Properties of (Hermitian) operators; Postulates of quantum mechanics (inc. superposition & meas); Expectation values and variance; Continuous-variable bases: coordinate representation, momentum basis; Quantization of a physical system; Schrödinger equation and temporal evolution; Qubit (two-level system); Two-system and entanglement; 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 a box; Particles in different potential wells: infinite and finite wells in 1D; Scattering and tunneling through barriers; Bloch's theorem; Bosons and fermions; Perturbation theory (non-degenerate); Time-dependent perturbation theory; Time dependence of operators: different pictures; Adiabatic theorem; 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: 24 h, exercises: 12 h, exam: 3 h + independent work

DETAILS

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 : 2022-2023 Autumn II
  2022-2023 Spring V
  2023-2024 Spring V

  Enrollment :

  Registration for Courses: Registration for courses will take place on Sisu (sisu.aalto.fi).

Description