The need for a wave equation, given the de Broglie relation for particles and Bohr’s spatially periodic description of atomic orbitals, is noted. A derivation of Schrödinger’s wave equation as motivated by the classical wave equations of Chaps. 3 and 4 follows. The three postulates of wave mechanics -that to every observable there corresponds an operator, that the only possible values which measurements can yield are the eigenvalues, and that average values can be predicted with the Schrödinger wave function — are given. The special role of the energy eigenfunctions as yielding stationary states, and of the coordinate eigenfunctions as yielding a physical interpretation of the wave function are described. There then follows the analysis of the propagation of a free particle in terms of a wave packet, which serves as a basis for illustrating the Heisenberg uncertainty principle. Sect. 6.4 explores the wave-particle duality and indetermin-ism, and ends up by showing that these do not upset our notions of an orderly world. Lastly, Sect. 6.5 outlines some of the wide range of phenomena that have been quantitatively interpreted by quantum mechanics. Among the problems, 6.14 illustrates time dependent phenomena in wave mechanics corresponding to the driven oscillator of classical mechanics.
KeywordsWave Function Quantum Mechanic Wave Equation Wave Packet Free Particle
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- H.A. Medicus: Fifty Years of Matter Waves, Physics Today (Feb. 1974)Google Scholar
- L.I. Schiff: Quantum Mechanics (McGraw-Hill, New York, 1968). This is a classic textbook on quantum mechanics. Many other good texts exist.Google Scholar
- A. Yariv: Quantum Electronics, Third Edition (John Wiley & Sons, New York 1987). A good place to look for applications of quantum mechanics in a very practical field.Google Scholar