Item description for Time-Dependent Density Functional Theory (Lecture Notes in Physics) by Miguel A.L. Marques...
Time-dependent density functional theory (TDDFT) is based on a set of ideas and theorems quite distinct from those governing ground-state DFT, but emphasizing similar techniques. Today, the use of TDDFT is rapidly growing in many areas of physics, chemistry and materials sciences where direct solution of the Schrdinger equation is too demanding. This is the first comprehensive, textbook-style introduction to the relevant basics and techniques.
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Est. Packaging Dimensions: Length: 9.45" Width: 6.14" Height: 1.57" Weight: 2.34 lbs.
Release Date Sep 25, 2006
ISBN 3540354220 ISBN13 9783540354222
Availability 59 units. Availability accurate as of May 30, 2017 07:26.
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The critical parts Dec 4, 2007
Normally on books covering relatively new techniques, some space is given, especially in the basic chapters (as opposed to applied -- in fact the basic chapters are really the most advanced) to problems, whether eexperimental or more fundamental and theoretical, with the model. Such is hardly to be found here. In fact a recent article I saw mentioned that oscillator strengths found in 'velocity' are often not identical with those found from 'lengths', i.e. transition momentum representation versus transition moment representation. In reality, this cannot be true. Thus, there is something fundamentally wrong with the method whenever this happens. It would be nice if a critical account of this were presented. In fact I believe it does all track down to the fact that in ALL DFT methods, one eschews complex-valued functions. In some cases, i.e. Klein-Gordan field-wavefunctions one can simply double up the number of variables, and it makes little difference. Here however, one cannit. The correct radiation Hamiltonian utilizes p/dot/A where A is the vector potential and p the electron momentum. The object over which this operator acts are *spinors*, if they are represented as real, they are 4x4 matrices, if they are represented as complex, they are 2-complex dimensional bivectors. Dirac was well aware that it is impossible to represent interaction with the electromagnetic field in a causal, relativistic theory linear in the covariant space-time derivatives using only real numbers. Q.E.D. Without some very fancy approximation methods, ANY DFT, including TDDFT, is bound to fail. Things get even worse with gauge invariance (perchance as in circular dichroism). Since the vector potential is not always a well defined object, people now talk about gauge connections of the U1 fibre bundle. This object IS well defined in a larger variety of problems. Unfortunately, it really does require one to keep trakc of phases in a complex space. Other relativistic effects could also be expected to suffer with DFT treatments.