Quantum dynamics, NWI-SM295, April 2019, 3EC

Lecturer: Gerrit Groenenboom

Please read the announcement of April 13, 2020 on brightspace

Summary: you can also do the quantum theoretical chemistry course this 4th quarter 2020, if you have not done it already.

April 8, 2020 version of : lecture notes

There will be three computer assignments (see below). To get started with the assignments there will be three computer classes (HG03.761):

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)

Last updated: June 9, 2019, by Gerrit C. Groenenboom, e-mail: gerritg at theochem dot ru dot nl