Two-state quantum system. Probabilistic interpretation and Schrodinger equation for the two-state state system. Examples of two state systems such as quantum interferometer (explanation of wave particle duality), quantum beats (elementary spectroscopy) are studied. Two level systems are extended to the N level systems. One dimensional continuous systems; Schrodinger equations of motion; solution for 1D harmonic oscillator, and the infinite and finite square well potential; scattering from barrier and step potential. Applications such as quantum wires, quantum dots, tunnelling.