Chem210 Quantum Mechanics

Course information:

All the information you need for this course will be accessible from this site.

Course materials will be made available as the course progresses

Tutorials and homework form part of this course and are examinable. Extra reading and on-line material is associated with each lecture, and is optional. If you want to find out still more please contact me, I can recommend a wider variety of texts, including those which cover material in more detail.

Need some help!

Check the recommended text for this course:

Molecular Quantum Mechanics, Peter Atkins and Ronald Friedman, Oxford University Press, 4th or 5th edition.

Ask your class mates and friends

This is good for you and them, teaching and explaining something really helps you understand it yourself. You could also get together with your friends and try to talk material through, discussing material is actually a good way to learn.

Contact Me

I'm very happy to revceive questions via e-mail:

Mathematics Revision

(updated for 2025)

In this course you will need to be able to differentiate, integrate and know about complex numbers.

The *minimum* entry maths requirement is very low for chemistry, this means you will need to put some extra work in if you have not taken maths with calculus at university level

important you can check through a self test to see if you need to do some revision,
revision self test pdf
if you cannot do these you need to do some work before the course starts. This document also includes the exact chapters and exercises to work from in the Engineering Mathematics text book below.

I strongly recommend Engineering Mathematics: a Foundation for Electronic, Electrical, Communications and Systems Engineers, 4th edition or later, by Anthony Croft, Robert Davison, Martin Hargreaves and James Flint, Pearson, 2012.

Don't be put off by the title! this is a good resource and it is available on-line from the library

More generally recommended reading from this textbook:

• Chapter 9: Complex Numbers
• Chapter 10 & 11: Differentiation
• Chapter 13 & 14: Integration
• Chapter 19: Ordinary differential equations, specifically section 19.5
• Chapter 25: Functions of several variables, specifically 15.1-25.3 covering partial derivatives

slides from the introductory lecture for chem210, pdf

Other resources:

Maths for Chemists a RSC tutorial chemistry text, Martin Cockett and Graham Doggett, RSC publishing, an e-version is available from the library.

Maths for Chemists book from Birmingham and Leeds universities distributed by the Royal Society of Chemistry covering the very basic principles link

Atkins Physical Chemistry in particular the Appendix "Mathematical techniques"

The Chemistry Maths Book, Erich Steiner, Oxford University Press, Oxford, UK 2008

Lecture 1: Introduction and Classical Mechanics

(updated for 2025)

1. notes for the lecture: pdf
2. QM equations sheet: pdf
3. inclass activity answers: pdf
4. online-activity 1 video: spherical polar coordinates
5. online-activity 2 video: spring harmonic oscillator
6. online-activity 3: molecular vibrations HCl vibration and N₂ vibration
7. wikipedia on different types of (classical) spring
8. a 2021 journal article Highs and Lows of Bond Lengths: Is There Any Limit? you might need to be on campus or have VPN on to see the whole article

Lecture 2: Operators

(updated for 2025)

1. notes for the lecture: pdf
2. inclass activity answers: pdf
3. problems answers: pdf
4. online-activity 1 video: quantum mechanical operators
5. online-activity 2 video: eigenvalue equations
6. online-activity 3 video: the commutator

Lecture 3: Waves

(updated for 2025)

1. notes for the lecture: pdf
2. in-class activity answers: pdf
3. problems answers: pdf
4. lecture wave1: energy not position moves in a wave
5. lecture wave2: longitudinal vs transverse waves
6. more wave animations!(do scroll down)
7. lecture wave3: compression wave
8. lecture wave4: circular wave
9. lecture wave5: springs and waves are related
10. online-activity 1 video sin and cos curves
11. lecture wave6: interfering waves forming a standing wave
12. interference patterns of two light sources, you control the separation: link
13. additional link: Science Learning Hub, University of Waikato

Lecture 4: Core concepts

(updated for 2025)

1. notes for the lecture: pdf
2. on-line activity video: normalisation
3. on-line activity video: expectation value
4. in-class activity answers: pdf
5. problems answers: pdf
6. Schrödinger's cat
   • wiki on Schrodinger's cat
   • A twist on Schrodinger's Cat Scientific American, 2020
   • Schrodinger's kittens small particles, not macrosopic but not atomic, 2018
   • Physics World 2019

Assignment:

(updated for 2025)

1. released 16th Aug, due 5pm Tue 23rd Sept handed in at Chemistry reception
2. assignment: pdf

Lecture 5: The Free Electron

(updated for 2025)

1. notes for the lecture: pdf
2. on-line activity video: prove psi is a solution
3. on-line activity video: momentum of a free particle
4. in-class activity answers: pdf
5. problems answers: pdf
6. make your own sum of cos curves wavepacket! a contribution from a student Joshya Keegan who has made a small javascript simulator for us, this opens in a new window, draws a Cartesian plane and has a simple input box, add in the values of k that you would like separated by a space.
   See the github project here

Lecture 6: The Particle in a Box

(updated for 2025)

1. notes for the lecture: pdf
2. in-class activity answers: pdf
3. on-line activity video: setting up the potential and solving the Wave equation
4. on-line activity video: boundary conditions for the wavefunction
5. on-line activity video: normalise the wavefunction
6. problems answers: pdf
7. a web-site which goes through all the details of matching wavefunctions and derivates across the potential boundaries: link
8. animation of a particle hitting a barrier: link
9. paper on particle in a box plasmon excitations in nanoparticles: P. Jain, J. Phys. Chem. Lett. 2014, 5, 18, p3112-3119, DOI:10.1021/jz501456t

Lecture 7: The Particle on a Ring

(updated for 2025)

1. notes for the lecture: pdf
2. QM equations sheet: pdf
3. in-class activity answers: pdf
4. additional link: moments of inertia
5. on-line activity video: prove psi is a solution to the particle on a ring
6. on-line activity video: normalise psi for the particle on a ring wavefunction
7. problems answers: pdf
8. additional link: porphyrin
9. additional link: spherical harmonics

Lecture 8: The Harmonic Oscillator

(updated for 2025)

1. notes for the lecture: pdf
2. in-class activity answers: pdf
3. problems answers: pdf
4. additional link: Gaussian functions
5. additional link: Hermite polynomials

Tutorial

(updated for 2025)

1. write the equation (defining all variables) you would need to evaluate (but don't evaluate it!) if asked a problem based on the following:
   • an eigenvalue equation
   • the Wave equation
   • show that Ψ is a solution
   • normalisation
   • determine the momentum of Ψ?
   • determine the expectation value of operator X
   • what is the probability?
2. what you should know for the wavefunction for each potential "form": free electron, particle in a well, particle on a ring, harmonic oscillator ...
   • be able to fully describe the functional form Ψ
   • be able to show it is an eigenfunction
   • be able to normalise the wavefunction
   • be able to show what happens when operating with the momentum and other operators
   • be able to show an expectation value using the wavefunction
   • be able to show determine a probability using the wavefunction