PHYS-C0252 - Quantum Mechanics, Lecture, 1.11.2021-14.12.2021

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Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.

LEARNING OUTCOMES

After completing the course the student

  1. Is familiar with the 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 analyze one-dimensional harmonic oscillator.
  6. Can solve the eigenstates of the one-dimensional harmonic oscillator. 
  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: 01.11.2021 - 14.12.2021

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:

    Postulates of quantum mechanics. Operators, eigenvalues and eigenfunctions. Expectation values and variance. Schrödinger equation. Properties of Hermitian operators. Qubit (two-level system). The superposition principle. Heisenberg's uncertainty principle. Commutator relations. Conserved quantities. Dirac notation. Hilbert space. Free particle and continuum energy spectrum.  Particle in a potential well and discrete energy spectrum. Creation and annihilation operators and their relation to one-dimensional harmonic oscillator. The temporal evolution of quantum states and expectation values. Perturbation theory. Time development of expectation values (Ehrenfest's principle). The density matrix. Rotating frame. 

Assessment Methods and Criteria

  • valid for whole curriculum period:

    Teaching methods: lectures and exercises 

    Assessment methods: exercises and exam

Workload

  • valid for whole curriculum period:

    Lectures: 24 h, exercises: 12 h, exam: 3 h + independent work

DETAILS

Study Material

  • valid for whole curriculum period:

    Several options for recommened reading (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
Prerequisites

FURTHER INFORMATION

Further Information

  • valid for whole curriculum period:

    Teaching Period:

    2020-2021 Autumn II

    2021-2022 Autumn II

    Course Homepage: https://mycourses.aalto.fi/course/search.php?search=PHYS-C0252

    Registration for Courses: In the academic year 2021-2022, registration for courses will take place on Sisu (sisu.aalto.fi) instead of WebOodi.

    Registration via WebOodi.

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