Quantum Mechanics I PHY 513: Quantum Theory I - Suraj @ LUMS [PDF]

Core for physics MS students. Pre-requisites: PHY 104: Modern Physics; Linear algebra and differential equations. None f

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PHY 212: Quantum Mechanics I PHY 513: Quantum Theory I Instructor: Muhammad Sabieh Anwar

Year: 2014-15

Office:

Email: [email protected]

Semester: Fall

Office Hours:

Category: Undergrad

Course Code: PHY 212 Credits: 3

Course Title: Quantum Mechanics 1/Quantum Theory 1

Website: https://physlab.lums.edu.pk/index.php/Quantum_Mechanics_Teaching_Fall2015 Lecture format: Per week, there are two 75 minutes lectures and one 90 minutes tutorial. ____________________________________________________________________________ Course Description: Quantum Mechanics is the cornerstone of physics. This introductory course for undergraduates and graduates is meant to motivate the students about quantum states and their dynamics and present mathematically consistent, useful, pertinent and accurate descriptions of low energy systems. The ordering we will follow in this course is unusual because we will start with simpler, two dimensional systems (spins) and describe their time evolution. Later, we move on to continuous variable systems (particle in a box, hydrogen atom, harmonic oscillator). We will present examples and applications throughout.

Learning outcomes: At the conclusion of this course, students should be able to: 1.

Identify the difference between classical and quantum systems

2.

Identify similarities between physically disparate physical systems, and should be able to present a unified picture of states based on state vectors and density matrices and dynamics based on unitary operators.

3.

Should be able to predict the outcomes of a quantum measurement and the probabilistic nature of the outcomes.

4.

Realize selected applications of quantum mechanics.

Course Status: Core for Physics Majors and Physics Minors. Core for physics MS students. Pre-requisites: PHY 104: Modern Physics; Linear algebra and differential equations. None for graduates.

Text books: Quantum Mechanics: Theory and Experiment by Mark Beck. (Primary textbook) A Modern Approach to Quantum Mechanics by John S Townsend. (Primary textbook)

Grading scheme:

Undergraduates Quizzes 20% Homeworks: 10% Mid-Term 30% Final Exam 40% Graduates Quizzes 10% Homeworks: 10% Term paper: 10% Mid-Term 30% Final Exam 40% The instructor has the liberty of varying these grade assignments by 5%.

Tentative Course Schedule & Topics:

Week

Topic

Some Particular Applications

1A

Classical polarization: Description of classical

Analysis of light by polarizer-

polarization in terms of Jones calculus

analyzer arrangements, interference

1B

Quantum States: Description of pure quantum states, orthogonality, measurement and analogies with classical states of polarized light

2-3

Operators and quantum measurement: Hermitian

Zeno effect, quantum logic

operators, projection operators, unitary and rotation

gates and quantum circuits

operators, Schrodinger equation, meaning of quantum measurement, complementarity and indeterminacy of quantum states 4

Spin 1/2 systems: The Stern-Gerlach experiment, spin states, commutation relations

5

Schrodinger's Equation: Time evolution operator,

Spin-1/2 inside a magnetic

the Schrodinger equation

field, magnetic resonance, neutrino oscillations

6

7, 8A

Angular Momentum: addition of angular

Arbitrary spin systems, spin of

momentums, rotation operators revisited,

a photon

Two particle systems: States of two-particle

Applications of symmetrization

systems, Entanglement, Bell's inequalities, local

postulate in spin isomers,

realism, density matrices

teleportation or tests of local realism

8B

Mid-Term

9-10

Wave Mechanics: Position and momentum

Infinite, finite square wells,

operators, representations, wave packets

tunneling, some applications of tunneling in electronic devices, slow and fast light (dispersion)

11

The Harmonic oscillator: creation and annihilation

Squeezed light

operators, energy spectrum and wave functions, Fock states and photons, coherent states 12-13

Three-dimensional wave mechanics: central potential, hydrogen atom, quantum numbers, multielectron atoms

14

Review and Final Exam

Origin of paramagnetism

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