# Part IB - Quantum Mechanics

## Lectured by J. M. Evans, Michaelmas 2015

These notes are not endorsed by the lecturers, and I have modified them (often significantly) after lectures. They are nowhere near accurate representations of what was actually lectured, and in particular, all errors are almost surely mine.

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# Contents

- V Full version
- 0 Introduction
- 1 Wavefunctions and the Schrodinger equation
- 2 Some examples in one dimension
- 2.1 Introduction
- 2.2 Infinite well –- particle in a box
- 2.3 Parity
- 2.4 Potential well
- 2.5 The harmonic oscillator
- 3 Expectation and uncertainty
- 3.1 Inner products and expectation values
- 3.2 Ehrenfest's theorem
- 3.3 Heisenberg's uncertainty principle
- 4 More results in one dimensions
- 4.1 Gaussian wavepackets
- 4.2 Scattering
- 4.3 Potential step
- 4.4 Potential barrier
- 4.5 General features of stationary states
- 5 Axioms for quantum mechanics
- 5.1 States and observables
- 5.2 Measurements
- 5.3 Evolution in time
- 5.4 Discrete and continuous spectra
- 5.5 Degeneracy and simultaneous measurements
- 6 Quantum mechanics in three dimensions
- 6.1 Introduction
- 6.2 Separable eigenstate solutions
- 6.3 Angular momentum
- 6.4 Joint eigenstates for a spherically symmetric potential
- 7 The hydrogen atom