Page 10 - PRINCIPLES OF QUANTUM MECHANICS as Applied to Chemistry and Chemical Physics

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The wave function

Quantum mechanics is a theory to explain and predict the behavior of particles
such as electrons, protons, neutrons, atomic nuclei, atoms, and molecules, as
well as the photon±the particle associated with electromagnetic radiation or
light. From quantum theory we obtain the laws of chemistry as well as
explanations for the properties of materials, such as crystals, semiconductors,
superconductors, and super¯uids. Applications of quantum behavior give us
transistors, computer chips, lasers, and masers. The relatively new ®eld of
molecular biology, which leads to our better understanding of biological
structures and life processes, derives from quantum considerations. Thus,
quantum behavior encompasses a large fraction of modern science and tech-
nology.
Quantum theory was developed during the ®rst half of the twentieth century
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through the efforts of many scientists. In 1926, E. Schrodinger interjected wave
mechanics into the array of ideas, equations, explanations, and theories that
were prevalent at the time to explain the growing accumulation of observations
of quantum phenomena. His theory introduced the wave function and the
differential wave equation that it obeys. Schrodinger's wave mechanics is now
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the backbone of our current conceptional understanding and our mathematical
procedures for the study of quantum phenomena.
Our presentation of the basic principles of quantum mechanics is contained
in the ®rst three chapters. Chapter 1 begins with a treatment of plane waves
and wave packets, which serves as background material for the subsequent
discussion of the wave function for a free particle. Several experiments, which
lead to a physical interpretation of the wave function, are also described. In
Chapter 2, the Schrodinger differential wave equation is introduced and the
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wave function concept is extended to include particles in an external potential
®eld. The formal mathematical postulates of quantum theory are presented in
Chapter 3.

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