To introduce the formalism and foundational concepts of quantum mechanics.

(LO1) Demonstrate an understanding of how quantum systems are described by wave functions, and how probabilities are extracted.

(LO2) Solve the Schrödinger Equation and describe the properties of a particle confined to fundamental potentials.

(LO3) Demonstrate an understanding of operators and eigenvalue problems in quantum mechanics and apply knowledge to solve simple problems.

(LO4) Understand how orbital angular momentum and spin angular momentum are described in quantum mechanics and apply knowledge to solve simple problems.

(LO5) Demonstrate an understanding of how quantum mechanics can be used to describe the Hydrogen atom, including fine structure.

(LO6) Describe and explain the structure of the periodic table and how this relates to Pauli’s Exclusion Principle.

(LO7) Solve one-dimensional problems involving scattering, transmission, reflection, and tunnelling of quantum probability amplitudes.

(S1) Problem solving skills

(S2) Collaborative learning

1. Introduction of quantum mechanics, small systems, action, complex numbers, formalism of complex wave-functions, experimental motivation.   
2. Operators and measurements, commutators and mutual disturbance.
3. Waveforms.
4. Forces and potential energy, total energy, energy diagrams, potential wells, free particle 
5. De Broglie wave, momentum operators, localisation, normalisation. 
6. Wave equation, simplest wave function,  eigenvalue equation, stationary states, wave packets.
7. Wave functions, stationary states 
8. Time dependent Schrödinger equation, time independent Schrödinger equation, probability density.
9. Wave functions and probability densities. 
10. Bound states, square well potential, harmonic oscillator, diatomic molecules.
11. Zero point energy, uncertainty principle.
12. 3-D potentials and energy degeneracies, angular momentum, central potentials, Hydrogen atom. 
13.  Angular momentum operators, 3-D harmonic oscillator.
14. Solving Schrödinger Equation for Hydrogen atom.
15. Stern Gerlach experiment and intrinsic spin.
16. Quantum numbers (n, l, m_l, m_s), Pauli Exclusion Principle, Electron shell configurations.
17. Central field approximation and multi-electron atoms in the periodic table (basic overview).
18. Hydrogen Fine Structure.
19. Zeeman Effect and g-factors.
20. Quantum scattering, quantum flux conservation, potential steps.
21. Probability current density, continuity of wave functions across potential step boundaries. 
22. Potential steps and barriers, reflection and transmission of quantum flux, barrier penetration and tunnelling, transmission and reflection
of flux at potential steps, penetration depth.

Teaching Method 1 - Lectures, revision of those and Q&A, delivered on Campus - lectures recorded and available on VLE.

Description: Lecture to entire cohort on all course topics over. Attendance Recorded: Yes.
Notes: = Nominal 1 x 2hr lectures/week

Teaching Method 2 - Workshops delivered on campus.
Description: Weekly problem-solving classes to learn together with guidance from staff and receive feedback. 
Attendance Recorded: Yes
Notes: = 12 x 2hr Workshops