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Quantum Oscillators
eBook Publisher: John Wiley & Sons
Imprint: Wiley
Format: ePub Encrypted (DRM)
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An invaluable reference for an overall but simple approach to the complexity of quantum mechanics viewed through quantum oscillators
Quantum oscillators play a fundamental role in many areas of physics; for instance, in chemical physics with molecular normal modes, in solid state physics with phonons, and in quantum theory of light with photons. Quantum Oscillators is a timely and visionary book which presents these intricate topics, broadly covering the properties of quantum oscillators which are usually dispersed in the literature at varying levels of detail and often combined with other physical topics. These properties are: time-independent behavior, reversible dynamics, thermal statistical equilibrium and irreversible evolution toward equilibrium, together with anharmonicity and anharmonic couplings.
As an application of these intricate topics, special attention is devoted to infrared lineshapes of single and complex (undergoing Fermi resonance or Davydov coupling) damped H-bonded systems, providing key insights into this rapidly evolving area of chemical science.
Quantum Oscillators is a long overdue update in the literature surrounding quantum oscillators, and serves as an excellent supplementary text in courses on IR spectroscopy and hydrogen bonding. It is a must-have addition to the library of any graduate or undergraduate student in chemical physics.
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| Title of eBook: Quantum Oscillators | |
| Release Date: 04-18-2011 | |
| Publisher: Wiley |
This eBook download is available in the following formats:
| Parent title | Quantum Oscillators |
|---|---|
| Encrypted (DRM) | Yes |
| SKU | 9781118018019 |
| File size | 5155 |
| Security | n/a |
| Printing | Not allowed |
| Copying | Not allowed |
| Read aloud | No Sys requirements Download reader |
| Devices | Samsung Tablet, Apple Ipad & Iphone, Barnes & Noble Nook, Kobo eReader, Aluratek Libre, Iliad, Nokia, Blackberry, Hanlin |
| Note | Excellent navigation features are available via Adobe such as bookmarks and a quick access table of contents. Text search is easily accessible. An Adobe DRM-protected file is different than a pdf file in that it uses Adobe DRM (Digital Rights Management) technology, which authors and publishers use to protect their content from illegal online distribution and to set certain privileges such as restrictions on copying and printing. |
Quantum Oscillators
Chapter One
BASIC CONCEPTS REQUIRED FOR QUANTUM MECHANICS
In order to summarize the quantum basis required for the study of oscillators, it is necessary to define some mathematical notions concerning the properties of state spaces, particularly the concepts of linear operators, kets, bras, Hermiticity, eigenvalues, and eigenvectors of linear operators involved in the formulation of the different postulates. The first two sections of this chapter are devoted to this. However, it is possible to pass directly to the third section leaving for later the lecture of the previous one.
1.1 BASIC CONCEPTS OF COMPLEX VECTORIAL SPACES
1.1.1 Kets, bras, and scalar products
Quantum mechanics deals with state spaces, that is, vectorial spaces involving com- plex scalar products that are generally of infinite dimension. Any element of these spaces is named a ket and symbolized |...>| by inserting inside it a free notation allowing one to clearly identify this ket; for instance, |[Psi]k>1 or |n.
Since the space of states is vectorial, and if the kets |[Psi]1> and |[Psi]2> belong to the same state space, then the ket |[Phi]> defined by the linear superposition
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where λ1 and λ2 are two scalars, belongs also to the same state space.
Now, to some ket |[Psi]> of the state space there exists a linear functional that associates with some another ket |[Phi]> of this space a complex scalar A[Phi][Psi], which is the scalar product of |[Psi]> by |[Psi]>. This may be written
A[Phi][Psi] =
This linear functional, which is denoted . The bra
...
