1. 321 Quantum MechanicsUnit 1 Quantum mechanics unit 1 Foundations of QM Photoelectric effect, Compton effect, Matter waves The uncertainty principle The Schrödinger eqn. in 1D Square well potentials and 1D tunnelling The harmonic oscillator

2. 321 Quantum MechanicsUnit 1 Last time Photons Photoelectric effect Compton effect Matter waves de Broglie relations Electron diffraction Waves related to probability www.le.ac.uk/physics -> people -> Mervyn Roy

3. 321 Quantum MechanicsUnit 1 Heisenberg uncertainty principle Fundamental property of quantum systems Course 3210 Unit 3, Rae Chapter 4 Inherent uncertainties in predictions – or average spread of a set of repeated measurements Heisenberg - formulation of QM 1927, Nobel prize 1932

4. 321 Quantum MechanicsUnit 1 Example The position of a proton is known to within 10 -11 m. Calculate the subsequent uncertainty in its position 1 second later.

5. 321 Quantum MechanicsUnit 1

6. 321 Quantum MechanicsUnit 1

7. 321 Quantum MechanicsUnit 1 Example An atom in an excited state emits a photon of characteristic frequency,  The average time between excitation and emission is 10 -8 s. Calculate the irreducible linewidth of the transition.

8. 321 Quantum MechanicsUnit 1 Schrödinger equation Schrödinger - formulation of QM 1925-26, Nobel prize 1933

9. 321 Quantum MechanicsUnit 1 Schrödinger equation

10. 321 Quantum MechanicsUnit 1 Time independent Schrödinger equation

11. 321 Quantum MechanicsUnit 1 Constraints The wavefunction and its first derivative must be: Single valued Finite Continuous