The Simplest Applications of Quantum Mechanics

Davydov, A.S.

doi:10.1016/b978-0-08-020438-3.50010-0

Cited by 50 publications

(100 citation statements)

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“…Solitons in molecular and condensed-matter physics were discovered in the mid 1970s by Davydov [46,47] and Krumhansl and Schrieffer [42]. Since then, the idea has expanded into many areas such as phase transitions [42], electron transport in conducting polymers [48,49], energy transfer in molecular and biological systems [43,50,51], proton transfer in hydrogen-bonded systems [44,52,53], and others [54]. …”

Section: Introductionmentioning

confidence: 99%

Mechanisms of proton transfer in proteins: Localized charge transfer versus delocalized soliton transfer

Stuchebrukhov

2009

Phys. Rev. E

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Proton translocation coupled to redox chemistry is ubiquitous for membrane enzymes involved in energy generation in cells. In such enzymes, proton transport occurs in special proton conducting channels, which consist of a series of protonatable groups of the protein connected by chains of mobile water molecules. Here we discuss two possible mechanisms of proton transport along such structures: diffusion of a localized charge and delocalized soliton transitions, in which several protons are collectively shifted along a chain of hydrogen bonds.

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Section: Introductionmentioning

confidence: 99%

Mechanisms of proton transfer in proteins: Localized charge transfer versus delocalized soliton transfer

Stuchebrukhov

2009

Phys. Rev. E

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“…As concerns a single-injected electron, this density (with the accuracy to the e n product, which is a constant value for each protein molecule) in fact is determined by the velocity V . Taking into consideration the fact that current is to be determined based on the consideration on an injected electron, it is necessary to consider this electron as a free quasi-particle of the classic type within the conductivity band of the primary structure of the protein molecule [19–21]. In this case, each of the eigenvalues E s ( v , k ) for the energies of subzones is to be considered as a classic Hamiltonian of the wave pulse p = ℏ k [21, 22].…”

Section: Resultsmentioning

confidence: 99%

Current in the Protein Nanowires: Quantum Calculations of the Base States

Suprun¹,

Shmeleva²

2016

Nanoscale Res Lett

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It is known that synthesis of adenosine triphosphoric acid in mitochondrions may be only completed on the condition of transport of the electron pairs, which were created due to oxidation processes, to mitochondrions. As of today, many efforts were already taken in order to understand those processes that occur in the course of donor-acceptor electron transport between cellular organelles (that is, between various proteins and protein structures). However, the problem concerning the mechanisms of electron transport over these organelles still remains understudied. This paper is dedicated to the investigation of these same issues.It has been shown that regardless of the amino acid inhomogeneity of the primary structure, it is possible to apply a representation of the second quantization in respect of the protein molecule (hereinafter “numbers of filling representation”). Based on this representation, it has been established that the primary structure of the protein molecule is actually a semiconductor nanowire. In addition, at the same time, its conduction band, into which an electron is injected as the result of donor-acceptor processes, consists of five sub-bands. Three of these sub-bands have normal dispersion laws, while the rest two sub-bands have abnormal dispersion laws (reverse laws). Test calculation of the current density was made under the conditions of the complete absence of the factors, which may be interpreted as external fields. It has been shown that under such conditions, current density is exactly equal to zero. This is the evidence of correctness of the predictive model of the conductivity band of the primary structure of the protein molecule (protein nanowire). At the same time, it makes it possible to apply the obtained results in respect of the actual situation, where factors, which may be interpreted as external fields, exist.

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“…In difference from closed states, for scattering states, the probabilistic interpretation of wave functions remains valid only in the sense of relative probability [2] and the quadratical integrability condition for wave functions holds no more, namely, the wave function may be finite even at infinity, and the plane wave solution is a typical example. Taking into account this situation and the discussions given in the previous sections, we may draw the following conclusions for scattering states: For position-space wave functions, the conditions of single-valuedness, continuity, and finiteness11 remain unaltered, but here we mean the whole position space by the word "everywhere," whereas the quadratical integrability condition breaks down; for momentum-space wave functions, too, the quadratical integrability condition holds no more, whereas the other admissibility conditions, are, in general, more complicated depending on the concrete forms of the potential energy U(r), just as in the case of closed states.…”

Section: Scattering Statesmentioning

confidence: 99%

“…Really, the condition of quadratical integrability implies that the wave function @(r) and its first derivatives are finite and continuous almost everywhere, i.e., everywhere except in a set of measure zero. For certain physical systems such as the hydrogen atom, finiteness at the origin is usually assumed to avoid the anomalous solutions [2,8]. In such cases, finiteness is not based on the fundamental assumptions of quantum mechanics, but adapted to certain particular properties of the physical models.…”

Section: Closed States: Position-space Wave Functionsmentioning

confidence: 99%

“…Take the single-valuedness condition as an example. Some authors [2,3] argue that the single-valuedness condition is necessary to ensure that the orbital angular momenta are integrals and they do not provide a real basis for the single-valuedness condition, instead they propose an additional postulate (orbital angular momenta are integrals). This postulate, being valid only for certain particular physical models, should be taken as a consequence of the Schrodinger *"Everywhere" means "for all values of the coordinates that the particle can take."…”

Section: Introductionmentioning

confidence: 98%

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On the conditions for physical admissibility of Schrödinger wave functions

Pan

Sen

1991

Int J of Quantum Chemistry

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It is shown that the dispute about the conditions for physical admissibility of Schrodinger wave functions may be settled if the following two questions are clarified: (a) Are these conditions rooted in the foundations of quantum mechanics or invoked only for particular physical models? (b) Do we consider either the position-space wave function or the momentum-space wave function? Both the cases of closed states and scattering states are considered. Some general remarks about these conditions are made in the Conclusion.

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The Simplest Applications of Quantum Mechanics

Cited by 50 publications

References 0 publications

Mechanisms of proton transfer in proteins: Localized charge transfer versus delocalized soliton transfer

Mechanisms of proton transfer in proteins: Localized charge transfer versus delocalized soliton transfer

Current in the Protein Nanowires: Quantum Calculations of the Base States

On the conditions for physical admissibility of Schrödinger wave functions

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