Fundamentals of quantum mechanics: Wave-particle duality, lack of determinism and Born’s probabilistic interpretation; Wavefunction, Hilbert space, vectors and Linear operators, basis of the Hilbert space, observables in quantum mechanics: their eigenvalues and eigenvectors, time-independent Schrodinger's equation as eigenvalue problem: stationary states; Cauchy-Schwarz inequality and uncertainty principle – its consequences in quantum mechancis. Time-independent potentials: energy eigenstates, bound states and scattering states. Free-particle: issues with normalizabilty of the energy eigenstates and wavepacket, spectrum and its degeneracy: particle in a box, Harmonic oscillator - ladder operator. Rectangular and delta-function barriers: Scattering and tunneling. Orbital angular momenta: algebra and spherical harmonics. Hydrogen atom and its spectrum. Spin angular momentum. Spin-1/2 particle in a magnetic field: Stern-Gerlach experiment, Larmor precision, Zeemann effect.