14 - The Principles of Quantum Mechanics. I. Classical Waves and the Schrödinger Equation

Abstract

Classical mechanics is based on the laws of motion discovered by Sir Isaac Newton, and is also called Newtonian mechanics. It is now known to be accurate only for objects of relatively large mass and for relatively high energies, as it consists of theories with arbitrary assumptions of quantization, devised to explain phenomena that classical physics could not explain. This theory consists primarily of the black-body radiation theory of Planck, the photoelectric effect theory of Einstein, and the hydrogen atom theory of Bohr. De Broglie sought a physical justification for Bohr's assumption of quantization, and hypothesized that all particles move with a wavelike character with a wavelength. According to the concept of wave-particle duality, electrons and other objects have some of the properties of classical waves and some of the properties of classical particles. Schrödinger discovered a wave equation for these matter waves. The solutions to the time-independent Schrödinger equation for three example systems are presented: the particle in a hard box, the free particle, and the harmonic oscillator.