*June 14, 2024 version of :
lecture notes*

- Prospectus
- Schedule
- The lecture notes of the bachelor course Quantum Theoretical Chemistry give more details of bound state problems

- 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)

*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.

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.

- 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

- 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

You are allowed to prepare one double sided printout with equations and use it during the exam

- Atomic and Molecular Collisions (Belgrade lecture 2017)
- Introduction to time-independent scattering theory (lecture notes by Mark van der Loo)
- Inleiding verstrooiingstheorie (J. G. Snijders)
- Angular momentum theory (lecture notes Gerrit C. Groenenboom)
- Lecture Molecular rotations and vibrations (Ad van der Avoird)
- Lecture notes by Millard Alexander
- Time-dependent approach to semiclassical dynamics, E. J. Heller, J. Chem. Phys., 62, 154 (1975)
- The semiclassical way to molecular spectroscopy Eric J. Heller Accounts of chemical research, 14, 368 (1981)

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*Last updated: May 24, 2024, by Gerrit C. Groenenboom,
e-mail: gerritg at theochem dot ru dot nl
*