Quantum Mechanics Preface 1 Principles of Quantum Mechanics 1.1 Quantum States 1.2 The Schrodinger Equation 1.3 Conditions for Valid Wavefunctions 1.4 Expectation Values 1.5 Quantum Uncertainty 1.6 Probability Current 2 Quantum Mechanics in One Dimension 2.1 The Free Particle 2.2 Gaussian Wave Packets 2.3 The Infinite Square Well 2.4 Properties of Energy Eigenstates 2.5 Hermitian Operators 2.6 Commutators 2.7 Conservation Laws 3 The Quantum Harmonic Oscillator 3.1 Introduction to the Quantum Harmonic Oscillator 3.2 Solving the Quantum Harmonic Oscillator 3.3 Energy Eigenstates of the QHO 3.4 Solving the QHO with Ladder Operators 3.5 Ladder Operators 4 Quantum Mechanics in Multiple Dimensions 4.1 The 3D Quantum Harmonic Oscillator 4.2 Degeneracy 5 The Hydrogen Atom 5.1 The Hydrogen Hamiltonian 5.2 Solving the Hydrogen Atom 5.3 Energy Eigenstates of Hydrogen 5.4 Angular Momentum