Schrodinger Theory Research Articles

Approximate resolutions of the Schrodinger theory applying the WKB approximation for certain diatomic molecular interactions.

The Analyzing of energetic bond spectra of diatomic compounds is crucial to understanding theirqualities because it allows one to evaluate their attributes. Diatoms compounds' spectral properties andbound energies are presented in this study. These energies are found by solving the Schrodinger equationwhile making consideration of the employing of the Kratzer Feus potential. This study focuses on the calculation of bound states for diatomic molecules using the WKBapproximation. The final energy spectrum equation is utilized to compute the bound states of specificdiatomic molecules for varying quantum numbers n and l through the utilization of the Mathematicasoftware. The method produced the desired and anticipated results, as shown by a comparison of theeigenvalue results with earlier studies.

DNA sequencing using nanopores and kinetic proofreading

We discuss the feasibility of using a nanopore sandwich device to implement the principle of kinetic proofreading to discriminate incorrect hybridizing oligonucleotides on a target DNA or RNA. We propose a method of sequencing DNA or RNA using this approach. The design parameters for such a DNA sequencer are estimated from the Hopfield‐Ninio theory of kinetic proofreading and Schrödinger’s first‐passage‐time distribution function.

Uma sequência didática utilizando a literatura de cordel e a arte das histórias em quadrinhos para inserção de tópicos de Física Quântica no Ensino Médio

A inserção de tópicos de Física Moderna e Contemporânea (FMC) no Ensino Médio é um desafio no atual panorama do ensino de Física. Na perspectiva de colaborar com esse debate, apresenta-se, neste artigo, uma sequência didática utilizando material com elementos de expressão artística com o objetivo de auxiliar os professores do Ensino Médio na abordagem de tópicos de Mecânica Quântica voltados aos estudantes. A história em quadrinhos (HQs), Os moídos e pelejas desde o átomo clássico inté o átomo quântico, aborda interpretações básicas das teorias de Planck, Bohr, de Broglie e Schrödinger sobre a estrutura dos átomos. A experiência de aplicação aconteceu em uma turma do terceiro ano mediante uma sequência didática inspirada na Unidade de Ensino Potencialmente Significativa (UEPS), levando em consideração princípios da teoria cognitiva da aprendizagem significativa. Os resultados da experiência foram analisados em uma abordagem quali-quantitativa e indicaram um satisfatório avanço na desenvoltura dos estudantes, com isso, colaborando para o desenvolvimento de uma postura investigativa e demonstrando envolvimento com o material didático, comprometimento com o trabalho em equipe e, principalmente, compreensão inicial dos conceitos e fenômenos estudados. A contextualização do conteúdo em versos de cordel e ilustrações da HQs, mediante a aproximação entre Arte e Ciências, propiciou aos estudantes um pensar e estudar Física sob o viés da criatividade, bem como mais liberdade para o estímulo do desenvolvimento da capacidade imaginativa.

The Evolution of Consciousness

This paper presents a new and positive theory of evolution, as distinct from instancing certain unique features of the phenotype of whatever species, and asking the question 'How could this come about by natural selection of random genetic mutations'. Essentially this paper starts with the premise that intelligence and consciousness comes from the DNA, and that therefore these particular features of life must actually be embedded in the DNA. Once this premise is accepted then not only does the orthodox Neo-Darwinism as 'natural selection through random genetic mutations' appear an over-simplified, if not facile, explanation for the immense complexity and diversity to be found in Nature (which contrary to popular belief actually incudes human civilization as well), but also opens up the possibility that there really could be Intelligent Design coming from within the DNA itself. Erwin Schrodinger's theory of quantum biology that genetic mutations occur as discreet jumps according to the principles of quantum mechanics is also presented and explained.

Quantal density-functional theory in the presence of a magnetic field

Quantal density functional theory (Q–DFT) of electrons in an external electrostatic field is generalized to the added presence of a magnetostatic field. This Q–DFT constitutes the mapping from the interacting system of electrons in an external electrostatic and magnetostatic field in any state as described by Schrodinger theory to one of noninteracting fermions with the same density, physical current density, electron number, and canonical orbital and spin angular momentum. To formulate this Q–DFT, Schrodinger theory from the perspective of the individual electron via the corresponding ‘Quantal Newtonian’ first law is developed. It is shown that in addition to the external fields, each electron experiences an internal field which is comprised of components representative of electron correlations due to the Pauli exclusion principle and Coulomb interaction, the density, the kinetic effects, and a contribution due to the external magnetic field. These fields are derived from quantal sources that are expectations of Hermitian operators taken with respect to the system wave function. As such the intrinsic self-consistent nature of the Schrodinger equation is demonstrated. With the Schrodinger equation written in self-consistent form, the magnetic field, (in addition to the vector potential of the field component of the momentum), now appears explicitly in it. The ’Quantal Newtonian’ first law for the model system of noninteracting fermions is derived. It is shown that if the model fermions are subject to the same external potentials, then the only electron correlations that must be accounted for in the Q–DFT mapping are those of the Pauli principle, Coulomb repulsion and Correlation-Kinetic effects. The resulting local electron-interaction potential within Q–DFT is the work done in an effective field that is the sum of fields representative of these correlations. The corresponding many-body components of the total energy can be expressed in integral virial form in terms of the separate fields. To explicate this Q–DFT, it is applied to a quantum dot as represented by the exactly solvable two-dimensional Hooke’s atom in a magnetic field. A key observation is that as a result of the reduction in dimensionality due to the presence of the magnetic field, Correlation-Kinetic effects are significant.

The motive force of evolution based on the principle of organismal adjustment evolution

From the analysis of the existing problems of the prevalent theories of evolution, this paper discussed the motive force of evolution based on the knowledge of the principle of organismal adjustment evolution to get a new understanding of the evolution mechanism. In the guide of Schrodinger's theory - "life feeds on negative entropy", the author proposed that "negative entropy flow" actually includes material flow, energy flow and information flow, and the "negative entropy flow" is the motive force for living and development. By modifying my own theory of principle of organismal adjustment evolution (not adaptation evolution), a new theory of "regulation system of organismal adjustment evolution involved in DNA, RNA and protein interacting with environment" is proposed. According to the view that phylogenetic development is the "integral" of individual development, the difference of negative entropy flow between organisms and environment is considered to be a motive force for evolution, which is a new understanding of the mechanism of evolution. Based on such understanding, evolution is regarded as "a changing process that one subsystem passes all or part of its genetic information to the next generation in a larger system, and during the adaptation process produces some new elements, stops some old ones, and thereby lasts in the larger system". Some other controversial questions related to evolution are also discussed.

W Acana Sains Dalam Novel Supernova Episode Ksatria, Puteri, Dan Bintang Jatuh

This paper is aimed to describe the stories of Supernova 1 to identify the fiction and non• fiction dialectics and also to represent science aspect in Supernova novel Episode Ksatria, Puteri, dan Bintang Jatuh (Supernova 1) through the relationship of intertextuality. We can find five stories in novel Supernova 1, they are the stories about Ruben-Dhimas, Ferre-Rana-Arwin, Diva, Supernova, and classic fairy tale knight, princess, and falling star. The dialectics between fiction and non-fiction in Supernova I are found through some indications, such as cover, tittle, scientific process of writing method in fiction such as the use of footnote, the insert of bibliography and index, and also preface, the dynamic of character, events arragernent that make plot, mentioning 'keping' to change chapter. Science aspect in Supernova 1 are not only a pacth but they are represented in text structure. The transformation of science elements in novel Supernova 1 are more affirmative with hypogram that is referred by some expansion. That science elements are astronomy, chaos theory (it covers Lorenz butterflies and fractal geometri), Schrodinger, co-evolution, and non-linear theories.

Two- and Three-Particle Systems in Relativistic Schrödinger Theory

The relativistic Schrodinger theory (RST) for N-fermion systems is further elaborated with respect to three fundamental problems which must emerge in any relativistic theory of quantum matter: (i) emergence/suppression of exchange forces between identical/non-identical particles, (ii) self-interactions, (iii) non-relativistic approximation. These questions are studied in detail for two- and three-particle systems but the results do apply to a general N-particle system. As a concrete demonstration, the singlet and triplet configurations of the positronium groundstate are considered within the RST framework, including a discussion of the corresponding hyperfine splitting.

Ortho- and Para-helium in Relativistic Schrödinger Theory

The characteristic features of ortho- and para-helium are investigated within the framework of Relativistic Schrodinger Theory (RST). The emphasis lies on the conceptual level, where the geometric and physical properties of both RST field configurations are inspected in detail. From the geometric point of view, the striking feature consists in the splitting of the $$\mathfrak{u}(2)$$ -valued bundle connection $$\mathcal{A}_{\mu}$$ into an abelian electromagnetic part (organizing the electromagnetic interactions between the two electrons) and an exchange part, which is responsible for their exchange interactions. The electromagnetic interactions are mediated by the usual four-potentials A μ and thus are essentially the same for both types of field configurations, where naturally the electrostatic forces (described by the time component A 0 of A μ) dominate their magnetostatic counterparts (described by the space part A of A μ). Quite analogously to this, the exchange forces are as well described in terms of a certain vector potential (B μ), again along the gauge principles of minimal coupling, so that also the exchange forces split up into an “electric” type ( $$\rightsquigarrow B_{0}$$ ) and a “magnetic” type ( $$\rightsquigarrow {\bf B}$$ ). The physical difference of ortho- and para-helium is now that the first (ortho-) type is governed mainly by the “electric” kind of exchange forces and therefore is subject to a stronger influence of the exchange phenomenon; whereas the second (para-) type has vanishing “electric” exchange potential (B 0 ≡ 0) and therefore realizes exclusively the “magnetic” kind of interactions ( $$\rightsquigarrow {\bf B}$$ ), which, however, in general are smaller than their “electric” counterparts. The corresponding ortho/para splitting of the helium energy levels is inspected merely in the lowest order of approximation, where it coincides with the Hartree–Fock (HF) approximation. Thus RST may be conceived as a relativistic generalization of the HF approach where the fluid-dynamic character of RST implies many similarities with the density functional theory.

Using supermodels in quantum optics

Starting from supersymmetric quantum mechanics and related supermodels within Schrodinger theory, we review the meaning of self-similar superpotentials which exhibit the spectrum of a geometric series. We construct special types of discretizations of the Schrodinger equation on time scales with particular symmetries. This discretization leads to the same type of point spectrum for the referred Schrodinger difference operator than in the self-similar superpotential case, hence exploiting an isospectrality situation. A discussion is opened on the question of how the considered energy sequence and its generalizations serve the understanding of coherent states in quantum optics.

Self-Energy and Action Principle in Relativistic Schrödinger Theory

The mathematical framework of Relativistic Schrodinger Theory (RST) is generalized in order to include the self-interactions of the particles as an integral part of the theory (i.e. in a non-perturbative way). The extended theory admits a Lagrangean formulation where the Noether theorems confirm the existence of the conservation laws for charge and energy–momentum which were originally deduced directly from the dynamical equations. The generalized RST dynamics is applied to the case of some heavy helium-like ions, ranging from germanium (Z=32) to bismuth (Z=83), in order to compute the interaction energy of the two electrons in their ground-state. The present inclusion of the electron self-energies into RST yields a better agreement of the theoretical predictions with the experimental data.

Relativistic ionization energies of the helium-like ions

The ionization energies of the helium-like ions with nuclear charge numbers Z (2 < Z < 100) are calculated within the framework of Relativistic Schrodinger Theory (RST). The corresponding energy-eigenvalue problem in the Coulomb field of a point-like fixed nucleus is worked out in detail and numerical solutions for the ground state 1s 2 1 S 0 are obtained. The relativistic energy functional for the isotropic bound states is studied in detail, and its value upon the constructed ground-state solutions yields the ionization energy for both cases where the electronic self-energy is either included or neglected. The combination of the RST two-particle self-energy with the one-particte Lamb shift of QED yields predictions for the ionization energies, which for the relativistic domain (high nuclear charge numbers) agree well with the experimental data.

Calculation of tunnel splitting in a biaxial spin particle with an applied magnetic field

The level splitting formulae of excited states as well as ground state for a biaxial spin particle in the presence of an applied magnetic field are obtained in a simple way from Schrodinger theory. Considering the boundary condition of the wave function, we obtain the tunneling splitting of the energy levels for half-integral spins as well as for the integral spins. The results obtained are compared with those previously derived by complicated pseudoparticle methods and numerical calculation values.

Relativistic effects in bound two-particle systems

The predictions of relativistic Schrodinger theory (RST) for the relativistic effects in helium-like ions with high nuclear charge ( $Z\sim 30$ -80) are elaborated in the electrostatic approximation (i.e. neglection of the magnetic interactions). The corresponding RST results are found to meet with the experimental data and with the predictions of other theoretical approaches, provided an estimate of the (neglected) magnetic effects is taken into account. This suggests to carry through high-precision calculations (including the magnetic forces) in order to further test the physical significance of RST.

Quantum Entanglement in Relativistic Three-Particle Systems

The relativistic three-particle systems are studied within the framework of Relativistic Schrodinger Theory (RST), with emphasis on the determination of the energy functional for the stationary bound states. The phenomenon of entanglement shows up here in form of the exchange energy which is a significant part of the relativistic field energy. The electromagnetic interactions become unified with the exchange interactions into a relativistic U(N) gauge theory, which has the Hartree–Fock equations as its non-relativistic limit. This yields a general framework for treating entangled states of relativistic many-particle systems, e.g., the N-electron atoms.

Relativistic wave equations for many-particle quantum systems

In this paper, some concepts of nonrelativistic many-particle quantum mechanics (e.g., product states, density matrix) are generalized to the relativistic domain using a framework called relativistic Schrodinger theory (RST). By using a general ansatz, the RST framework is simplified considerably and some of its field equations are solved directly. The RST approach is then compared with nonrelativistic quantum mechanics (QM) for the case of a product state (conventional QM) and its RST analog. It is shown that relativistic wave equations can he derived from the RST formalism, so that they coincide in the nonrelativistic limit with the well-known Hartree equations.

Analytic Properties of a Specialq-Exponential Function

formula math. yields for q ∈ (0, 1) the so-called symmetric q-difference operator on C {0}. Holomorphic solutions to the fixed point problem of this q-difference operator and of Δ q 2 are elaborated. The analytic properties of the corresponding holomorphic functions are investigated. A link between the eigenfunctions and the q-Fourier transform by Koornwinder and Swarttouw on a q-linear grid is established. The relevance of the fixed point problem to discrete Schrodinger theory is briefly mentioned.

Relativistic Schrödinger Theory and the Hartree–Fock Approach

Within the framework of Relativistic Schrodinger Theory (RST), the scalar two-particle systems with electromagnetic interactions are treated on the basis of a non-Abelian gauge group U(2) which is broken down to the Abelian subgroup U(1)×U(1). In order that the RST dynamics be consistent with the (non-Abelian) Maxwell equations, there arises a compatibility condition which yields cross relationships for the links between the field strengths and currents of both particles such that self-interactions are eliminated. In the non-relativistic limit, the RST dynamics becomes identical to the well-known Hartree–Fock equations (for spinless particles). Consequently the original RST field equations may be considered as the relativistic generalization of the Hartree–Fock equations, and the “exchange interactions” of the conventional theory (induced by the anti-symmetrization postulate) do reappear here as ordinary gauge interactions due to a broken symmetry.

Basic Analogs of Schrödinger's Equation

Basic analogs of Schrodinger's equation are investigated on a so-called q-linear grid or basic linear grid. A ladder operator formalism for a discrete harmonic oscillator analog is developed with a representation in theweighted Hilbert space l 2 (Z) over the q-linear grid. The moment problem for the corresponding modified discrete q-Hermite polynomials of type II is revised. Conditions on the existence of a ladder operator formalism in connection with the considered moment problem are developed. The results are evaluated with respect to an application for purposes of discrete Schrodinger theory.

Two new symmetry-adapted perturbation theories for the calculation of intermolecular interaction energies

We outline two new symmetry-adapted perturbation theories (SAPTs) and present some results obtained with them. The first is superior to the symmetrized Rayleigh–Schrodinger (SRS) theory in that it corrects a fundamental defect of that theory, namely, that carried to infinite order the SRS theory cannot predict even the ground-state energy for most interacting atoms and molecules. The new theory includes correction terms which have a large cumulative effect, but which, order by order, make only small contributions. When applied to interacting closed-shell systems and truncated after first order in the wave function, it is equal in accuracy to the SRS theory. Thus, it provides both an understanding of why the SRS theory gives results of useful accuracy and justification for its continued use when truncated to low order. The second new SAPT also corrects the SRS theory's flaw, but achieves significantly greater accuracy than the SRS theory when truncated after first order in the wave function. Applied to the interaction between the open-shell Li and H atoms, a critical test case, the second theory gives the ground-state dissociation energy with an error of 1%, whereas the SRS theory is in error by 38%. The LiH molecule is a critical test case because its physical ground-state energy, like that of nearly all systems, lies in a continuum of accessible states which violate the Pauli exclusion principle.