Mathematical Introduction: Linear vector spaces, inner products, linear operators, eigenvalue problem, generalization to infinite dimensions.

Towards quantum mechanics: relevant experiments, wave particle duality, uncertainty principle, postulates of quantum mechanics, Schrodinger equation, probability current and conservation.

Simple one-dimensional potential problems: Free particle, particle in a box; scattering in step-potentials, transmission and reflection coefficients.

Harmonic oscillator: Obtaining eigenvalues and eigen functions using ladder operators. Angular momentum: Rotations in three dimensions, eigenvalue problem of L² and L_z.

Hydrogen atom: Eigenvalue problem, degeneracy of the spectrum, numerical estimates and comparison with experiments.