6. Quantum Mechanics

Electron has an important role in ferroelectric behaviour. In electromagnetics, electron is normally approximated as point charge. However, in fact, electron acts as quantum particle having wave-particle duality. In classical manner, the ideal progressive wave is expressed using trigonometric function. In order to incorporate wave property into particle, the relational formula between matter wave and photon energy are introduced. Based on the formula, the equation for quantum particle is derived. It is called Schrödinger equation, where position and time are included as variable. In real atom-based system, no quantum particle is completely isolated from others. Hence, quantum interactions between quantum particles are inserted into Schrödinger equation as the form of potential. When quantum interactions are independent from time, Schrödinger equation can be expressed as time-independent form. In quantum chemistry, time-independent form is normally called Schrödinger equation. Operators of kinetic energy and potential are called Hamiltonian. When normalised quantum wave function is applied, the total energy is directly given by operating Hamiltonian operator to quantum wave function. Since Hamiltonian is categorised as Hermitian operator, the total energy is represented by real number. Quantum wave function itself does not represent figure in three-dimensional space. Instead, the square of quantum wave function represents density of quantum particle. Quantum particle, electron, spreads as wave. For better understanding the relationship between quantum particle and quantum wave function, quantum tiger law is introduced.