Quantum Mechanical Model of Atom

Quantum mechanics — the branch of science built to satisfy both de Broglie's matter-wave duality and Heisenberg's uncertainty principle — was developed in 1926, independently, by Werner Heisenberg (starting from the uncertainty principle) and by Erwin Schrödinger (starting from wave motion). The wave-motion-based version, due to Schrödinger, is the one this chapter takes up. Schrödinger's fundamental equation of quantum mechanics, the Schrödinger (or wave) equation, is written $\hat{H}\psi = E\psi$, where $\hat{H}$ is a mathematical operator called the Hamiltonian, $\psi$ (psi) is the wave function, and E is the total energy of the system. Actually solving this equation is beyond the scope of this ch …