*April 8, 2020 version of :
lecture notes*

- Wed, 10 Apr 2019, 15:45-17:30 (bound state problems)
- Wed, 08 May 2019, 15:45-17:30 (tunneling)
- Wed, 29 May 2019, 15:45-17:30 (elastic scattering)

- Week 1
- Born-Oppenheimer approximation, 1st+2nd step
- Nonadiabatic coupling
- Rotation and vibration of diatom molecule

- Week 2, 16 April 2019
- Time-dependent Schroedinger equation, solution in finite basis
- Matrix exponentiation, functions of matrices

*Lecture notes: chapter 3, Griffith: Appendix on linear algebra* - Week 3, 23 April 2019
- Gaussian wave packet solution of the one dimensional time-dependent Schrodinger equation
- Flux-operator

- Week 4. 7 May 2019
- Time independent scattering in 1 dimension, tunneling
- Collinear A+BC elastic scattering
- Collinear A+BC inelastic scattering, coupled channels equation

- Week 5. 14 May 2019
- The central force problem
- Classical: Newton and Hamilton
- Angular momentum and impact parameter
- Plane waves and spherical waves
- Boundary conditions for 3D elastic scattering

*Lecture notes: chapter 11, 11.1, 11.2, 11.3* - Week 6
- Expansion of plane waves in partial waves
- Scattering amplitude and S-matrices
- Integral and differential cross sections

- Week 7
- Inelastic scattering

- Week 8
- Angular momentum theory
- Wigner D-matrix
- Spherical harmomic addition theorem

- 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,
normalization factor
)
- 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
(pdf,
answers-wk8.pdf)
)
- Angular momentum theory
- Wigner rotation matrices
- Spherical harmonic addition theorem

- Assignment 1: harmonic oscillator and Morse oscillator (pdf)
(Hint: 1 hartree = 219474.63 cm
^{-1}) - Assignment 2: tunneling through Eckart barrier (pdf), see also Carl Eckart, Phys. Rev., 35, 1303 (1930)
- Assignment 3: He+Xe elastic scattering (pdf)

- Lecture notes (version November 13, 2019)
- 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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