Need for quantum mechanics: The inadequacies of classical mechanics and need of quantum
mechanics. Matter waves: Matter waves and their statistical interpretation, Wave functions, State functions and
their basic property eg, Time-dependent Schrödinger equation and the operators: Superposition
principle, Physical interpretation of wave function and probability current density, Expectation values,
Schwartz inequality and proof of uncertainty principle, Wave packets, Linear operators. Eigen functions, Eigenvalues, Orthogonal systems, Expansion in eigenfunction and completeness relation, Hermitian operators, Simultaneous eigen functions, Commutators, Parity operator. Commutation rule, Equation of motion. Time independent Schrödinger equation: The concept of stationary states, Problems in one dimension- (i) Zero potential (the free particle case), (ii) Infinite square well potential (particle in a box), (iii) Potential step (reflectance and transmittance), (iv) potential barrier, (v) Rectangular potential well (vi) Periodic potential. and (vii) Linear harmonic oscillator. The Schrödinger equation for spherically symmetric potential: Angular momentum operators, The hydrogen atom.