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Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics)
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Spectral Methods in Chemistry and Physics - Applications to Kinetic Theory and Quantum Mechanics (Hardcover, 2015 ed.)
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Spectral Methods in Chemistry and Physics - Applications to Kinetic Theory and Quantum Mechanics (Hardcover, 2015 ed.)
Series: Scientific Computation
Expected to ship within 12 - 17 working days
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This book is a pedagogical presentation of the application of
spectral and pseudospectral methods to kinetic theory and quantum
mechanics. There are additional applications to astrophysics,
engineering, biology and many other fields. The main objective of
this book is to provide the basic concepts to enable the use of
spectral and pseudospectral methods to solve problems in diverse
fields of interest and to a wide audience. While spectral methods
are generally based on Fourier Series or Chebychev polynomials,
non-classical polynomials and associated quadratures are used for
many of the applications presented in the book. Fourier series
methods are summarized with a discussion of the resolution of the
Gibbs phenomenon. Classical and non-classical quadratures are used
for the evaluation of integrals in reaction dynamics including
nuclear fusion, radial integrals in density functional theory, in
elastic scattering theory and other applications. The subject
matter includes the calculation of transport coefficients in gases
and other gas dynamical problems based on spectral and
pseudospectral solutions of the Boltzmann equation. Radiative
transfer in astrophysics and atmospheric science, and applications
to space physics are discussed. The relaxation of initial
non-equilibrium distributions to equilibrium for several different
systems is studied with the Boltzmann and Fokker-Planck equations.
The eigenvalue spectra of the linear operators in the Boltzmann,
Fokker-Planck and Schroedinger equations are studied with spectral
and pseudospectral methods based on non-classical orthogonal
polynomials. The numerical methods referred to as the Discrete
Ordinate Method, Differential Quadrature, the Quadrature
Discretization Method, the Discrete Variable Representation, the
Lagrange Mesh Method, and others are discussed and compared. MATLAB
codes are provided for most of the numerical results reported in
the book - see Link under 'Additional Information' on the the
right-hand column.
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