PHYS30201
Mathematical Fundamentals of Quantum Mechanics
10
Semester 1
Undergraduate
Level 3
Michael Birse
Unit coordinator
1
FHEQ level (Framework for Higher Education Qualifications) ' Last part of a Bachelors '
European Credit Transfer & Accumulation System Rating : 5.0
<p>Mathematical Fundamentals of Quantum Mechanics (M)</p>
<p>Mathematical Fundamentals of Quantum Mechanics (M)</p>
<p>To develop an understanding of quantum mechanics and in particular the mathematical structures underpinning it.</p>
<p>On completion of the course, successful students should be able to:</p><p><br />1. Use Dirac notation to represent quantum-mechanical states and manipulate operators in terms of their matrix elements.<br />2. Solve a variety of problems with model and more realistic Hamiltonians, demonstrating an ability to use the mathematical underpinning of quantum mechanics.<br />3. Work with angular momentum operators and their eigenvalues both qualitatively and quantitatively.<br />4. Use perturbation theory and other methods to find approximate solutions to problems in quantum mechanics, including the fine-structure of energy levels of hydrogen.</p>
<ol>
<li>
<strong>The Fundamentals of Quantum Mechanics </strong>(6 lectures)</li>
</ol>
<p style="margin-left: 21.3pt">Postulates of quantum mechanics</p><p style="margin-left: 21.3pt">Time evolution: the Schrödinger equation and the time evolution operator</p><p style="margin-left: 21.3pt">Ehrenfest’s theorem and the classical limit</p><p style="margin-left: 21.3pt">The simple harmonic oscillator: creation and annihilation operators</p><p style="margin-left: 21.3pt">Composite systems and entanglement</p><p style="margin-left: 21.3pt"> </p>
<ol>
<li value="2">
<strong>Angular Momentum </strong>(7 lectures)</li>
</ol>
<p style="margin-left: 21.3pt">General properties of angular momentum</p><p style="margin-left: 21.3pt">Electron spin and the Stern-Gerlach experiment</p><p style="margin-left: 21.3pt">Higher spins</p><p style="margin-left: 21.3pt">Addition of angular momentum</p><p style="margin-left: 21.3pt">Vector Operators</p><p style="margin-left: 21.3pt"> </p>
<ol>
<li value="3">
<strong>Approximate methods I: variational method and WKB </strong>(3 lectures)</li>
</ol>
<p style="margin-left: 21.3pt">Variational methods</p><p style="margin-left: 21.3pt">WKB approximation for bound states and tunneling</p><p style="margin-left: 21.3pt"> </p>
<ol>
<li value="4">
<strong>Approximate methods II: Time-independent perturbation theory </strong>(5 lectures)</li>
</ol>
<p style="margin-left: 21.3pt">Non-degenerate and degenerate perturbation theory</p><p style="margin-left: 21.3pt">The fine structure of hydrogen</p><p style="margin-left: 21.3pt">External fields: Zeeman and Stark effect in hydrogen</p><p style="margin-left: 21.3pt"> </p>
<ol>
<li value="5">
<strong>The Einstein-Poldosky-Rosen “paradox” and Bell’s inequalities </strong>(1 lecture)</li>
</ol>
<p> </p>
1
Written exam
100%
<p>Feedback will be available on students’ solutions to examples sheets through examples classes, and model answers will be issued.</p>
MATH10212
Linear Algebra B
Pre-Requisite
Compulsory
PHYS20101
Introduction to Quantum Mechanics
Pre-Requisite
Compulsory
PHYS20252
Fundamentals of Solid State Physics
Pre-Requisite
Recommended
PHYS20672
Complex Variables and Vector Spaces
Pre-Requisite
Compulsory
<p>For recommneded theory units following this module please see PHYS40481 and 40682.</p>
N
<p>Shankar, R. Principles of Quantum Mechanics 2nd ed. (Plenum 1994)<br />Gasiorowicz, S. Quantum Physics, 3rd ed. (Wiley, 2003)<br />Mandl, F. Quantum Mechanics (Wiley, 1992)<br />Griffths, D. J. Introduction to Quantum Mechanics, 2nd ed (CUP, 2017)</p>
Assessment written exam
1.5
Lectures
22
0
76.5