Quantum dynamics, NWI-SM295, April 2023, 3EC
Lecturer: Gerrit Groenenboom
June 14, 2024 version of :
lecture notes
Computer assignment reports are due:
- Assignment 1: Friday, 26 Apr 2024; Harmonic oscillator and Morse oscillator (pdf)
(Hint: 1 hartree = 219 474.63 cm-1)
- Assignment 2: Friday, 24 May 2024; Tunneling through Eckart barrier (pdf),
see also Carl Eckart, Phys. Rev., 35, 1303 (1930)
- Assignment 3: Friday, 14 June 2024; He+Xe elastic scattering (pdf)
Python GUIs to play around with
To gain more insight and a feeling for scattering, we created Python GUIs for Assignments 2 and 3. The code itself is obfuscated, but can be run in any Python 3 environment, although it is dependent on several Python packages.
The GUI for Eckart Tunneling can be downloaded here as a .py file. This plots the Eckart barrier and corresponding scattering wave function. Variables can be adjusted for the numerical grid, the potential itself and for the propagation of a wave packet (an electron colliding with the barrier). All values are in atomic units.
The GUI for He-Xe scattering can be downloaded here. This plots the total elastic cross section, the radial scattering wave function, the differential cross section and angle-dependent wave function for the He-Xe potential. Blue lines in the ICS and DCS correspond to the contribution of a single L.
Instructions for computer assignment reports
The computer program must be handed in
together with a brief report (brightspace).
The report should contain enough detail so that
someone who has not seen the assignment can read the report and
understand which equations are solved by the computer program, and
how. All the parameters that were used must be given, so that it
would be possible to reproduce the results, without looking at the
program. There is no need, however, to include derivations and
general theory that can be found in the lecture notes. An
example of such a report (without the code though), is this
report on a particle-in-a-box time-dependent wave packet.
Also, carefully read the
Writing tips for a report.
In particular, read the checklist for report on that page. The abstract/introduction/conclusions etc
is not necessary for the computerassignment report.
Lectures
- Week 1
- Chapter 1 and 2 (may skip 1.4 and 1.5 at first), 3.1
- Rotation and vibration of diatom molecule
- Time-dependent Schroedinger equation, solution
in finite basis
- See also: QTC Chapter 3+4
- Week 2
- Chapter 3: 3.1, 3.2, 3.3. Also: Griffith: Appendix on linear algebra
- Matrix exponentiation, functions of matrices
- Free particles in one dimension
- Week 3
- Chapter 3: 3.4, 3.5, 3.6, 3.7, 3.8
- Gaussian wave packet solution of the
one dimensional time-dependent Schrodinger
equation
- Flux-operator
- Week 4
- Chapter 4.1, 4.2, 4.3; 5.1
- Time independent scattering in 1 dimension, tunneling
- Collinear A+BC elastic scattering
- Collinear A+BC inelastic scattering, coupled channels equation
- Chapter 6.1
- The central force problem
- Classical: Newton and Hamilton
- Angular momentum and impact parameter
- Week 5
- Chapter 7.1, 7.2, 7.3
- Plane waves and spherical waves
- Boundary conditions for 3D elastic scattering
- Week 6
- Chapter 7.3, 7.4
- Expansion of plane waves in partial waves
- Scattering amplitude and S-matrices
- Integral and differential cross sections
- Week 7
- Chapter 8, 8.1
- Inelastic scattering
- Week 8 [optional ]
- Angular momentum theory
- Wigner D-matrix
- Spherical harmomic addition theorem
Exercises
- Week 1 (pdf,
answers)
- Separating the center-of-mass motion
- Harmonic oscillator
- Morse oscillator
- Week 2 (pdf,
answers)
- Time-propagator
- Autocorrelation function and spectrum
- Week 3 (pdf,
answers,
normalization factor)
- Time wave packet for free particle
- Flux
- One-dimensional scattering
- Week 4 (pdf,
answers)
- Kinetic energy operator in 3D
- Coupled channels equation for collinear A+BC
- Week 5 (pdf,
answers)
- Plane waves and spherical waves
- Flux in spherical polar coordinates
- Week 6 (pdf, answers)
- Plane wave expansion
- Scattering amplitude and S-matrices
- Integral and differential cross sections
- Week 7 (pdf, answers)
- Atom-molecule and molecule molecule inelastic scattering
- S-matrices, scattering amplitude, and state-to-state
differential cross sections
- Week 8 [optional ]
(pdf, answers)
- Chapter 9
- Angular momentum theory
- Wigner rotation matrices
- Spherical harmonic addition theorem
Exam example
Exam 21 July 2014
You are allowed to prepare one double sided printout with
equations and use it during the exam
References
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Last updated: May 24, 2024, by Gerrit C. Groenenboom,
e-mail: gerritg at theochem dot ru dot nl