Quantum dynamics, NWI-SM295, April 2022, 3EC
Lecturer: Gerrit Groenenboom
June 9, 2022 version of :
lecture notes
Computer assignment reports are due:
- Assignment 1: Fr, 29 Apr 2022; Harmonic oscillator and Morse oscillator (pdf)
(Hint: 1 hartree = 219474.63 cm-1)
- Assignment 2: Fr, 27 May 2022; Tunneling through Eckart barrier (pdf),
see also Carl Eckart, Phys. Rev., 35, 1303 (1930)
- Assignment 3: Fr, 17 June 2022; He+Xe elastic scattering (pdf)
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)
- Born-Oppenheimer approximation, 1st+2nd step
- Nonadiabatic coupling
- Rotation and vibration of diatom molecule
- See also: QTC Chapter 3+4
- Week 2
- Chapter 3: 3.1, 3.2, 3.3. Also: Griffith: Appendix on linear algebra
- Time-dependent Schroedinger equation, solution
in finite basis
- 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-wk1.pdf
)
- Separating the center-of-mass motion
- Harmonic oscillator
- Morse oscillator
- Week 2 (pdf
, answers-wk2.pdf
)
- Time-propagator
- Autocorrelation function and spectrum
- Week 3 (pdf
, answers-wk3.pdf
)
- Time wave packet for free particle
- Flux
- One-dimensional scattering
- Week 4 (pdf
, answers-wk4.pdf
)
- Kinetic energy operator in 3D
- Coupled channels equation for collinear A+BC
- Week 5 (pdf
, answers-wk5.pdf
)
- Plane waves and spherical waves
- Flux in spherical polar coordinates
- Week 6 (pdf
, answers-wk6.pdf
)
- Plane wave expansion
- Scattering amplitude and S-matrices
- Integral and differential cross sections
- Week 7 (pdf
, answers-wk7.pdf
)
- Atom-molecule and molecule molecule inelastic scattering
- S-matrices, scattering amplitude, and state-to-state
differential cross sections
- Week 8 [optional ]
(pdf
, answers-wk8.pdf
)
- Chapter 9
- Angular momentum theory
- Wigner rotation matrices
- Spherical harmonic addition theorem
Exam example
Exam 21 July 2014
References
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Last updated: June 9, 2022, by Gerrit C. Groenenboom,
e-mail: gerritg at theochem dot ru dot nl