1. 321 Quantum MechanicsUnit 2 Quantum mechanics unit 2 The Schrödinger equation in 3D Infinite quantum box in 3D 3D harmonic oscillator The Hydrogen atom Schrödinger equation in spherical polar coordinates Solution by separation of variables Angular quantum numbers Radial equation and principal quantum numbers Hydrogen-like atoms Rae – Chapter 3

2. 321 Quantum MechanicsUnit 2 So far… Matter behaves like waves (photoelectric effect, Compton, de Broglie etc) 1D Schrödinger equation Physically acceptable solutions only possible for certain discrete values of the energy Energy level spacing qualitatively similar to atoms Predicted tunnelling / interference – seen experimentally quantumphysics.iop/org Unit 2 Move from 1D to 3D to obtain quantitative predictions

3. 321 Quantum MechanicsUnit 2 Definitions

4. 321 Quantum MechanicsUnit 2 3D relations

5. 321 Quantum MechanicsUnit 2

6. 321 Quantum MechanicsUnit 2 3D quantum box 10 % isosurface

7. 321 Quantum MechanicsUnit 2

8. 321 Quantum MechanicsUnit 2 Quantum box in reality P. Offermans et al, Phys. Rev. B 72 165332 (2005) InAs/AlAs quantum dot