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 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: 26.04.2023 - 08.06.2023
Teacher in charge (valid for whole curriculum period):
Teacher in charge (applies in this implementation): 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:
Prerequisites
valid for whole curriculum period:
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 VEnrollment :
Registration for Courses: Registration for courses will take place on Sisu (sisu.aalto.fi).