Page 223 - Principles and Applications of NanoMEMS Physics

Appendix A

QUANTUM MECHANICS PRIMER

A.1 Introduction

In this appendix we present some of the salient point of quantum
mechanics (QM) of relevance to the material in this book. These include the
basic laws governing quantum systems, the harmonic oscillator and
quantization, creation and annihilation operators, the second quantization
formalism,and field operators.

A.2 Some Basic Laws Governing Quantum Systems

Phenomena occurring at microscopic scales is governed by quantum
mechanics (QM) [60]. According to QM, all the information regarding a
microscopic particle (e.g., momentum and position) is contained in its
wavefunction, ψ . This wavefunction obeys an operator equation, namely,
Schrödinger’s equation, and is determined by the total energy of the particle.
The possible energy states of the particle are given by the solutions to the
stationary Schrödinger’s equation,
ˆ
H ψ = E ψ , (A.1)
ˆ
where H is the Hamiltonian operator, which embodies the total energy of
the particle and is composed of the sum of its kinetic and potential energies,
and E is its eigenvalue. Since the result of measuring energy are real values,
ˆ
ˆ
H = H , i.e., H is hermitian. In general, there can be a multitude of
ˆ
†