**Answers in LaTeX for
the exercises of week 1, 2, 3, 4, 5, and 6, including questions in the corresponding Chapters are available below.**

**At the bottom of the page there are instructions for the computer assignment reports.**

**Hints and intermediate results for the computer assignments are available:**

computer assignment 1 | Hand in before exam |

computer assignment 2 | Hand in before exam |

computer assignment 3 | May be handed in after the exam |

**March 29, 2020: bug fixed in clebsch_gordan.m**

Lecturer: Prof. Gerrit C. Groenenboom

- Week 1
- Chapter 1, 2, and 3 of the Lecture notes
- Topics
- Review of quantum mechanics for particle in one dimension
- Hermitian operators
- "Diatomic molecule" in one dimension

- Exercise (Answers-wk1.pdf, typo in Eq. (30) fixed on 25-Mar-2020)
- Set up variational calculation of anharmonic vibration in harmonic oscillator basis

- Computer assignment 1: variational calculation

- Week 2
- Diatomic molecules in three dimensions, classically
- Diatomic molecules in three dimensions, quantum mechanically
- Exercise (Answers-wk2.pdf - including all exercises in Chapter 4)

- Week 3
- Angular momentum theory
- Exercise (Answers-wk3.pdf)

- Week 4, Chapter 7
- Atom-diatom system
- Angular momentum coupling
- Exercise (Answers-wk4.pdf)

- Week 5, Chapter 8
- Atom-diatom: potential energy matrix elements
- Legendre expansion of potential
- Gauss-Legendre quadrature
- Spherical harmonics addition theorem
- Clebsch-Gordan series of Wigner D-matrices
- (Exercises in text chapter 8)
- Exercise (version April 7, 2020) (Answers-wk5.pdf [Eqs. (3), (4), fixed April 7, 2020])

- Week 6, Chapter 9
- Two-fold symmetries
- Permutation symmetry, bosons & fermions
- Parity
- Symmetry adapted basis sets
- Selection rules
- Exercise (version Mar 11, 2020) (Answers-wk6.pdf)

- Computer assignment 1: variational calculation
- Computer assignment 2: numerical solution of 1D problem
- Computer assignment 3: variational calculation atom-diatom system

There are more hints for writing reports here. In particular, read the "checklist for report". The abstract/introduction/conclusions etc is not necessary for the computerassignment report.

- Write down the Hamiltonian of a small molecule or a molecular complex in a suitable coordinate system to describe rotation and vibration
- Use angular momentum theory and group theory to setup suitable basis functions for a variational calculation of molecular energy levels
- Write small computer programs to solve the time-independent and time-dependent Schroedinger equation to compute rotational and vibrational states and compute spectra an other properties of these systems.
- Derive the proper functional form for intermolecular interactions using first and second order perturbation theory
- Compute energy shifts due to external electric and magnetic fields

- Coordinate systems, in particular Jacobi coordinates
- The nuclear kinetic energy operator in internal coordinates
- Angular momentum operators and states
- Wigner rotation matrices
- Angular momentum coupling and Clesch-Gordan coefficients
- Integrals over Wigner rotation matrices
- Elementary group theory and the use of symmetry
- The use of discretization to solve the anharmonic vibrational oscillator

The lecture notes, computerassignments, and topics of each week are available on the website: https://www.theochem.ru.nl/qtc

This course focuses on bound states of molecules. Collisions of molecules or "quantum scattering" is the topic of the master course on Quantum Dynamics (NWI-SM295). The study of nuclear dynamics requires potential energy surfaces, which are found by solving of the electronic SchrÃ¶dinger equation. This is the topic of the master course "Quantum Chemistry" (NWI-MOL406).

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*Last updated: 29-Mar-2020, by Gerrit C. Groenenboom.*