Book contents
- Frontmatter
- Contents
- Preface
- 1 Classical mechanics vs. quantum mechanics
- 2 Basic postulates and mathematical tools
- 3 Wave/particle duality and de Broglie waves
- 4 Particles at boundaries, potential steps, barriers, and in quantum wells
- 5 The harmonic oscillator and photons
- 6 The hydrogen atom
- 7 Multi-electron ions and the periodic table
- 8 Interaction of atoms with electromagnetic radiation
- 9 Simple molecular orbitals and crystalline structures
- 10 Electronic properties of semiconductors and the p-n junction
- 11 The density matrix and the quantum mechanic Boltzmann equation
- References
- Index
2 - Basic postulates and mathematical tools
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- 1 Classical mechanics vs. quantum mechanics
- 2 Basic postulates and mathematical tools
- 3 Wave/particle duality and de Broglie waves
- 4 Particles at boundaries, potential steps, barriers, and in quantum wells
- 5 The harmonic oscillator and photons
- 6 The hydrogen atom
- 7 Multi-electron ions and the periodic table
- 8 Interaction of atoms with electromagnetic radiation
- 9 Simple molecular orbitals and crystalline structures
- 10 Electronic properties of semiconductors and the p-n junction
- 11 The density matrix and the quantum mechanic Boltzmann equation
- References
- Index
Summary
Basic scientific theories usually start with a set of hypotheses or “postulates.” There is generally no logical reason, apart from internal consistency, that can be given to justify such postulates absolutely. They come from ‘revelations’ in the minds of ‘geniuses,’ most likely with hints from Nature based on extensive careful observations. Their general validity can only be established through experimental verification. If numerous rigorously derived logical consequences of a very small set of postulates all agree with experimental observations without exception, one is inclined to accept these postulates as correct descriptions of the laws of Nature and use them confidently to explain and predict other natural phenomena. Quantum mechanics is no exception. It is based on a few postulates. For the purpose of the present discussion, we begin with three basic postulates involving: the “state functions,” “operators,” and “equations of motion.”
In this chapter, this set of basic postulates and some of the corollaries and related definitions of terms are introduced and discussed. We will first simply state these postulates and introduce some of the related mathematical tools and concepts that are needed to arrive at their logical consequences later. To those who have not been exposed to the subject of quantum mechanics before, each of these postulates taken by itself may appear puzzling and meaningless at first. It should be borne in mind, however, that it is the collection of these postulates as a whole that forms the foundations of quantum mechanics.
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- Chapter
- Information
- Fundamentals of Quantum MechanicsFor Solid State Electronics and Optics, pp. 8 - 32Publisher: Cambridge University PressPrint publication year: 2005