Module Details

The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title Quantum and Atomic Physics I
Code PHYS203
Coordinator Prof M D'Onofrio
Physics
Monica.Donofrio@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2020-21 Level 5 FHEQ First Semester 15

Aims

To introduce students to the concepts of quantum theory. To show how Schrodinger's equation is applied to bound states (well potentials, harmonic oscillator, hydrogen atoms, multi-electron atoms) and particle flux (scattering) . To show how quantum ideas provide an understanding of atomic structure.


Learning Outcomes

(LO1) At the end of the module the student should have an understanding of the reasons why microscopic systems require quantum description and statistical interpretation.

(LO2) At the end of the module the student should have knowledge of the Schrodinger equation and how it is formulated to describe simple physical systems.

(LO3) At the end of the module the student should have understanding of the basic technique of using Schrodinger's equation and ability to determine solutions in simple cases.

(LO4) At the end of the module the student should have understanding of how orbital angular momentum is described in quantum mechanics and why there is a need for spin.

(LO5) At the end of the module the student should have understanding how the formalism of quantum mechanics describes the structure of atomic hydrogen and, schematically, how more complex atoms are described.


Syllabus

 

Course overview:- Breakdown of classical physics, quantisation, discrete energy levels  Operators and Measurement; commutators  Complex wave-functions  Forces, potential energy, de Broglie wave  Wave equation, eigenvalue equation, stationary states  Schrodinger equation, wave function, probability density  Bound states, localisation, potential wells  Infinite well potential, finite well potential  Harmonic oscillator, 1D and 3D potential  Angular momentum and central potential  Generic solution of Schrodinger equation for central potential, conservation of angular momentum, angular momentum quantization  Hydrogen atom potential, discrete energy level  Many-electron atoms, intrinsic spin, quantum numbers  Magnetic dipole moments, spin-orbit energy, atomic fine structure  First order perturbation theory, Zeeman effect  Quantum flux, scattering at potential steps  Potential barrier, penetration and tunnelli ng 
1  Introduction of quantum mechanics, small system, action   Complex numbers, formalism of complex wave-fucntions   
2  Operators and measurements, commutators and mutual disturbance  Operator equation 
3  Blackbody radiation, ultraviolet catastrophe  Discrete energy levels, atomic line spectra  Wave-particle duality  
4  Waveforms  Operators and observables  Measurement, uncertainty principle
6  Forces and potential energy, total energy  Energy diagrams, potential wells  Free particle 
7  De Broglie wave, momentum operators  Localisation, normalisation 
8  Wave equation, simplest wave function  Eigenvalue equation, stationary states  Wave packet 
9  Wave functions  Stationary states 
10  Time dependent Schrodinger equation  Time independent Schrodinger equation  Probabi lity density 
11  Wave functions and probability densities 
12  Bound states, localisation  Square well potential  Harmonic oscillator, diatomic molecule 
13  Harmonic oscillator, wave functions and energies  Zero point energy, uncertainty principle 
14 3-D potentials and energy degeneracies  Angular momentum and central potentials  Hydrogen atom 
15  Angular momentum operators  3-D harmonic oscillator 
16  Many electron atoms, quantum numbers  Stern Gerlach experiment, intrinsic spin  Electron shells, configurations 
17  Elements and electronic configurations  Electronic transitions, spectroscopy 
18  Spin-orbit coupling, H atom fine structure  Periodic table, exclusion principle  Zeeman effect, spatial quantisation 
19  Spectroscopic notation, transitions  Zeeman splitting  First order pertur bation theory  Zeeman effect 
20  Quantum scattering  Quantum flux conservation  Potential steps
21  Probability current density, conservation  Continuity of wave functions across potential step boundaries 
22  Potential steps and barriers  Reflection and transmission of quantum flux  Barrier penetration and tunnelling  Transmission and reflection of flux at potential steps   Penetration depth  
23-24  General revision


Teaching and Learning Strategies

Teaching Method 1 - Lecture
Description:
Teaching Method 2 - problem classes
Description:


Teaching Schedule

  Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL
Study Hours 24

        24

48
Timetable (if known)              
Private Study 102
TOTAL HOURS 150

Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Exam There is a resit opportunity. Standard UoL penalty applies for late submission. This is an anonymous assessment.  120 minutes    70       
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Problem Classes Standard UoL penalty applies for late submission. This is not an anonymous assessment.  12 x 2 hour problem     30       

Recommended Texts

Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.