In this chapter, we first discuss the fundamentals of the Schrödinger equation, which is the governing equation of quantum mechanics. Then, we perform some calculations necessary to understand the physical properties of gases. The topics are the particle-wave duality of a microscopic object, Schrödinger equation for a single free particle, Schrödinger equation in the presence of potential, Born’s probabilistic interpretation of the wave function, expected values of physical quantities, stationary state, translational motion of a particle moving freely in a box, harmonic oscillation of a particle, rotational motion of a particle, a particle bound to the Coulomb potential created by a fixed point charge, and spin.