This course gives a deeper insight into quantum mechanics, beyond that of a freshman course. The course builds upon the worldwide extensively used book of Griffiths. The Schrödinger wave function: The Schrödinger equation, probability, probability current. The time-independent Schrödinger equation (2 lectures): Stationary states; the infinite square well; harmonic oscillator: algebraic method. The free particle, motion of Gaussian wave packet; bound states and scattering states: the finite square well. The formalism of quantum mechanics: Hilbert space, vectors and operators; observables as Hermitian operators; eigenfunctions of a Hermitian operators; bases in Hilbert space, Dirac notation. Quantum mechanics and angular momentum (2 lectures): the radial Schrödinger equation, the hydrogen atom, the radial wave function, the spectrum of hydrogen. Angular momentum: algebraic treatment, eigenvalues, eigenfunctions. Spin, spin 1/2, addition of spins. Time-independent perturbation theory (2 lectures): Non-degenerate first-order perturbation theory, second-order energies degenerate perturbation theory. Applications: the Zeeman effect, Stark effect, the hyperfine structure of hydrogen. The variational principle: Theory; harmonic oscillator, anharmonic oscillator, hydrogen ground state; the ground state of Helium. Quantum dynamics (2 lectures): Two-level systems, the perturbed system, time-dependent perturbation theory, Rabi oscillations. Emission and absorption of radiation, the lifetime of an excited state, Fermi’s golden rule, selection rules. Scattering (2 lectures): Classical scattering theory, quantum scattering theory and partial wave analysis, phase shifts. The Lippmann-Schwinger equation, the first Born approximation, Coulomb scattering. Identical particles: Two-particle systems, bosons and fermions, Pauli principle, hydrogen molecule. Quantum mechanical pictures: Heisenberg picture, interaction picture.