Basic Quantum Mechanics

This chapter introduces key concepts and basic aspects of quantum mechanics (QM) for describing the essential part of materials science related to atoms and their subatomic particles, such as electrons (e-), protons (e+), neutrons, and photons (packet of energy in the form of light). The mathematical description of the particle motion incorporates quantization of energy, wave-particle duality, and the uncertainty principle. Regarding particle motion, the deterministic classical mechanics describes the particle at a macroscale, while the probabilistic quantum mechanics treats the particle at an atomic scale. The main emphasis in the chapter is to describe the abstract behavior of a wavelike particle in a confined volume of a metal specimen using Schrodinger equation that describes, in particular, the three-dimensional (3D) time-dependent wavefunction Y(r,t) with spatial (space r = x,y,z) and temporal (time t) variables. Subsequently, the 3D framework of Y(r,t) is simplified to a one-dimensional (1D) time-independent wavefunction y(x). The Heisenberg uncertainty principle (HUP) is also described as part of quantum mechanics related to measurements of two variables, such as position and velocity of a traveling particle in a quantum mechanical system.