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Bohmian theory

It is worth noting that although we obtained the total energy (4.123) in the Bohmian mechanics context, it showcases a clear electronic density dependency, not under a density functional (as DFT would require) but merely as a spatial function, which is a direct reflection of the entanglement behavior of Bohmian theory through the involvement of a quantum potential. However, in most cases, and especially for atomic systems, Eq. (4.123) will yield numerical values under custom density function realizations. [Pg.194]

The theories that should feature prominently in the understanding of chemical effects have been summarized in this volume, without demonstrating their application. The way forward has been indicated by Primas [67] and in the second volume of this work the practical use of modern concepts such as spontaneous symmetry breaking, non-local interaction, bohmian mechanics, number theories and space-time topology, to elucidate chemical effects will be explored. The aim is to stimulate renewed theoretical interest in chemistry. [Pg.522]

Q Time-Dependent Density Functional Theory from a Bohmian Perspective... [Pg.105]

The purpose of this chapter is to show and discuss the connection between TD-DFT and Bohmian mechanics, as well as the sources of lack of accuracy in DFT, in general, regarding the problem of correlations within the Bohmian framework or, in other words, of entanglement. In order to be self-contained, a brief account of how DFT tackles the many-body problem with spin is given in Section 8.2. A short and simple introduction to TD-DFT and its quantum hydrodynamical version (QFD-DFT) is presented in Section 8.3. The problem of the many-body wave function in Bohmian mechanics, as well as the fundamental grounds of this theory, are described and discussed in Section 8.4. This chapter is concluded with a short final discussion in Section 8.5. [Pg.107]

An alternative way to obtain the quantum trajectories is by formulating the Bohmian mechanics as a Newtonian-like theory. Then, Equation 8.29 gives rise to a generalized Newton s second law ... [Pg.114]

In Bohmian mechanics, the way the full problem is tackled in order to obtain operational formulas can determine dramatically the final solution due to the context-dependence of this theory. More specifically, developing a Bohmian description within the many-body framework and then focusing on a particle is not equivalent to directly starting from the reduced density matrix or from the one-particle TD-DFT equation. Being well aware of the severe computational problems coming from the first and second approaches, we are still tempted to claim that those are the most natural ways to deal with a many-body problem in a Bohmian context. [Pg.117]

Bohmian mechanics refers to the ontological interpretation of quantum theory pioneered by Bohm [4]. The mathematical structure of the theory is not affected by the different interpretation and the same formalism adopted before [7] will be used here. [Pg.59]

The chemistry community, understandably, failed to respond at all, even though Bohmian mechanics probably holds the key to the development of a theory of chemistry, soundly based on quantum theory and relativity. The problem with molecular structure is resolved by the ontological interpretation of quantum-mechanical orbital angular momentum and the key to chemical reactivity and reaction mechanism is provided by the quantum potential function. [Pg.284]

The theories of quantum mechanics and relativity and the concepts underlying these theories are unfamiliar territory for many chemists. To prepare the ground for a reassessment of the chemical importance of these theories against the background of Bohmian mechanics, the relevant concepts have recently been presented from a chemical perspective [7]. Constant reference to this earlier work will be made here. Important equations, discussed and... [Pg.284]

The new theories that spring from the application of Bohmian mechanics to chemical problems reveal a close connection between chemical phenomena and the attributes of space-time. The most fundamental principle of chemistry is the periodic classification of the elements in terms of natural numbers. Examined against the background of number theory a deeper level of periodicity that embraces all nuclides is revealed and found to relate on a cosmic scale to an involution in space-time structure. [Pg.285]

Virtually no aspect of chemistry is left untouched by the new insight gained through consideration of Bohmian mechanics, number theory and symmetry. A preliminary analysis of some of these aspects are presented here in an effort to stimulate further research, that may happen once familiarity with the new approach overcomes traditional scepticism. Most of the material in this book has been published in somewhat different form before. Chapters 1, 2, 4, 5, and 6 are elaborations based on recent review articles [8, 9, 10, 11] by the author and included here with permission by the relevant publishers. [Pg.285]

J.T. Cushing, A. Fine and S. Goldstein (eds.) Bohmian Mechanics and Quantum Theory An... [Pg.371]

Bohmian quantum theory charge waves chemical action chemical reactivity chemical softness... [Pg.350]


See other pages where Bohmian theory is mentioned: [Pg.129]    [Pg.69]    [Pg.129]    [Pg.69]    [Pg.246]    [Pg.286]    [Pg.282]    [Pg.302]    [Pg.165]    [Pg.347]    [Pg.533]    [Pg.167]    [Pg.622]    [Pg.187]    [Pg.2]    [Pg.561]   
See also in sourсe #XX -- [ Pg.129 ]




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