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1. Opintojakson nimi

Kvanttimekaniikka I

Kvantmekanik I

Quantum Mechanics I

2. Opintojakson tunniste (koodi)

FYS2018

Aikaisemmat leikkaavat opintojaksot 53716 Kvanttimekaniikka I, 10 op.

3. Opintojakso pakollisuus/valinnaisuus

Opintojaksosta vastaa fysikaalisten tieteiden kandiohjelma.

Opintojakso kuuluu pakollisena teoreettisen fysiikan aineopintokokonaisuuteen (FYS2300). Muilla fysikaalisten tieteiden opintosuunnilla opintojakson voi sisällyttää valinnaisiin aineopintoihin.

Opintojakso on tarjolla muiden koulutusohjelmien opiskelijoille. Muiden koulutusohjelmien opiskelijat voivat sisällyttää opintojakson fysikaalisten tieteiden opintokokonaisuuteen (FYS1900), teoreettisen fysiikan opintokokonaisuuteen (FYS1500), tai fysiikan aineopintokokonaisuuteen (FYS2700).


Bachelor's programme in physical sciences is responsible for the course.

The course is compulsory for students completing intermediate studies in theoretical physics (FYS2300) and optional for other study tracks. 

The course is available to the students from other degree programmes.

4. Opintojakson taso (alempi/ylempi/tohtori /eurooppalaisen viitekehyksen(EQF) tasot 6,7,8)

Kanditaso=alempi korkeakoulututkinto/EQF-taso 6

5. Opintojakson suositeltu suoritusajankohta/vaihe

The recommended time for completion: third year. This course should be taken after FYS2003 Introduction to Quantum Physics and FYS2012 Mathematical Methods in Physics IIa (and possibly FYS2013 Mathematical Methods in Physics IIb).

6. Opintojakson järjestämisajakohta lukukauden/ periodin tarkkuudella

The course is offered every year in the autumn term, periods I-II.

7. Opintojakson laajuus opintopisteinä

10 op

8. Opintojaksosta vastaava opettaja

Waldemar Kulig (waldemar.kulig@helsinki.fi)

9. Opintojakson osaamistavoitteet

Student is able to operate in Hilbert space and knows the probabilistic interpretation of quantum mechanics. Student knows the Dirac notation and algebra of Hermitian operators. Student is familiar with time evolution of wave function and is able to switch between the Schrödinger and Heisenberg picture of QM. Student is able to solve the Schrödinger equation for model problems in 3D. Student is familiar with spin, spin states, spin operators, and Pauli matrices. Student can calculate the Clebsch-Gordan coefficients and is familiar with superposition of orbital momenta. Student is able to apply the non-degenerate perturbation theory to model systems.

10. Opintojakso toteutus

Weekly lectures, independent work, solutions of exercises submitted weekly and graded by teaching assistants, exercise sessions with teaching assistants.

11. Edeltävät opinnot tai edeltävä osaaminen

FYS2003 Introduction to Quantum Physics and FYS2012 Mathematical Methods in Physics IIa

12. Suositeltavat valinnaiset opinnot

FYS2015 Statistical MechanicsFYS2016 Electrodynamics I and FYS2013 Mathematical Methods in Physics IIb

13. Opintojakson sisältö

1. Hilbert space and probabilistic interpretation of QM.

2. States and operators in QM. Dirac notation.

3. Hermitian operators and matrix representation.

4. Time evolution: Schrödinger and Heisenberg pictures of QM.

5. 1D harmonic oscillator, creation and annihilation operators, and coherent states.

6. Gerlach-Stern experiment, ½-spin states, spin precession in magnetic field.

7. Two-state model, ammonia molecule in electric field, NMR/MRI (time-dependent magnetic field).

8. Schrödinger equation in 3D (free particle, infinite spherical well, harmonic oscillator).

9. Hydrogen atom.

10. Identical particles and multi-particle states. Tensor product.

11. Addition of the angular momentum and Clebsch-Gordan coefficients.

12. Introduction to time-independent perturbation theory.

14. Suositeltava tai pakollinen kirjallisuus

Principles of Quantum Mechanics, R. Shankar, second edition, Springer (mandatory).

Introduction to Quantum Mechanics, D. Griffiths, second edition, Cambridge University Press (mandatory).

15. Oppimista tukevat aktiviteetit ja opetusmenetelmät

Weekly lectures, independent work, solutions of exercises submitted weekly and graded by teaching assistants, exercise sessions with teaching assistants.

16. Arviointimenetelmät ja –kriteerit sekä arvosteluasteikko

Course is completed either by submitting exercise problems and solving the exam problems or alternatively by the final exam. The grade is determined in a way agreed at the beginning of the course.

17. Opetuskieli

Lectures and instructions are given in English.






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