Digital holographic imaging via direct quantum wavefunction reconstruction

Wavefunction is a fundamental concept of quantum theory.Recent studies have shown surprisingly that wavefunction can be directly reconstructed via the measurement of weak value.The weak value based direct wavefunction reconstruction not only gives the operational meaning of wavefunction,but also provides the possibility of realizing holographic imaging with a totally new quantum approach.Here,we review the basic background knowledge of weak value based direct wavefunction reconstruction combined with recent experimental demonstrations.The main purpose of this work focuses on the idea of holographic imaging via direct wavefunction reconstruction.Since research on this topic is still in its early stage,we hope that this work can attract interest in the field of traditional holographic imaging.In addition,the wavefunction holographic imaging may find important applications in quantum information science.

Wavefunction and energy of the 1s^2 2sns configuration in a beryllium atom

A new set of trial functions for 1s^22sns configurations in a beryllium atom is suggested. A Mathematica program based on the variational method is developed to calculate the wavefunctions and energies of 1s^22sns （n = 3 - 6） configurations in a beryllium atom. Non-relativistic energy, polarization correction and relativistic correction which include mass correction, one- and two-body Darwin corrections, spin-spin contact interaction and orbit-orbit interaction, are calculated respectively. The results are in good agreement with experimental data.

WAVEFUNCTIONS OF L-S COUPLING FERMION SYSTEM(Ⅰ): SINGLE-l

In this paper. it is discussed how to constrnct wavefunctions of L-S couplingfermion system, which are classified by group chain A recurrent formula of fractional parentage coefficients with fixedseniority is also given.

WAVEFUNCTIONS OF L-S COUPLING FERMION SYSTEM (Ⅱ):DOUBLE■-l

The wavefunctions of L-S coupling fermion system, which are classified by group chain U(4ι1 + 4ι2 + 4) Us(2)×(U L(2ι+ 2ι2 + 2) O(2ι1 + 2ι2 + 2) O(2ι+1) ×O(2ι2 + 1) O1 (3)×O2 (3) O(3)), are constructed through introducing generalized pairs coupled by fermions with different ι. With the help of the fractional parentage coefficients of single-ιfermion system, the author obtains the corresponding fractional parentage coefficients of double-ιfermion system.

Shannon Entropy as a Measurement of the Information in a Multiconfiguration Dirac-Fock Wavefunction

Discrete Shannon entropy is applied to describe the information in a multiconfiguration Dirac Fock wavefunction. The dependence of Shannon entropy is shown as enlarging the configuration space and it can reach saturation when there are enough configuration state wavefunctions to obtain the convergent energy levels; that is, the calculation procedure in multiconfiguration Dirae Fock method is an entropy saturation process. At the same accuracy level, the basis sets for the smallest entropy are best able to describe the energy state. Additionally, a connection between the sudden change of Shannon information entropies and energy level crossings along with isoelectronic sequence can be set up, which is helpful to find the energy level crossings of interest in interpreting and foreseeing the inversion scheme of energy levels for an x-ray laser.

Comparison of electron transmittances and tunneling currents in an anisotropic TiN_x/HfO_2/SiO_2/p-Si(100) metal-oxide-semiconductor(MOS) capacitor calculated using exponential- and Airy-wavefunction approaches and a transfer matrix method

Analytical expressions of electron transmittance and tunneling current in an anisotropic TiNx/HfO2/SiO2/p-Si（100） metal-oxide-semiconductor （MOS） capacitor were derived by considering the coupling of transverse and longitudinal energies of an electron. Exponential and Airy wavefunctions were utilized to obtain the electron transmittance and the electron tunneling current. A transfer matrix method, as a numerical approach, was used as a benchmark to assess the analytical approaches. It was found that there is a similarity in the transmittances calculated among exponential- and Airy-wavefimction approaches and the TMM at low electron energies. However, for high energies, only the transmit- tance calculated by using the Airy-wavefunction approach is the same as that evaluated by the TMM. It was also found that only the tunneling currents calculated by using the Airy-wavefunction approach are the same as those obtained under the TMM for all range of oxide voltages. Therefore, a better analytical description for the tunneling phenomenon in the MOS capacitor is given by the Airy-wavefunction approach. Moreover, the tunneling current density decreases as the titanium concentration of the TiNx metal gate increases because the electron effective mass of TiNx decreases with increasing nitrogen concentration. In addition, the mass anisotropy cannot be neglected because the tunneling currents obtained under the isotropic and anisotropic masses are very different.

Mott physics, sign structure, ground state wavefunction, and high- Tc superconductivity

In this article I give a pedagogical illustration of why the essential problem of high-Tc superconductivity in the cuprates is about how an antiferromagnetically ordered state can be turned into a short-range state by doping. I will start with half-filling where the antiferromagnetic ground state is accurately described by the Liang Doucot-Anderson （LDA） wavefunction. Here the effect of the Fermi statistics becomes completely irrelevant due to the no double occupancy constraint. Upon doping, the statistical signs reemerge, albeit much reduced as compared to the original Fermi sta- tistical signs. By precisely incorporating this altered statistical sign structure at finite doping, the LDA ground state can be recast into a short-range antiferromagnetic state. Superconducting phase coherence arises after the spin correlations become short-ranged, and the superconducting phase transition is controlled by spin excitations. I will stress that the pseudogap phenomenon naturally emerges as a crossover between the antiferromagnetic and superconducting phases. As a characteristic of non Fermi liquid, the mutual statistical interaction between the spin and charge degrees of freedom will reach a maximum in a high-temperature ＂strange metal phase＂ of the doped Mott insulator.

Strength of Intramolecular Hydrogen Bonds

The concept of resonance-assisted hydrogen bonds(RAHBs)highlights the synergistic interplay between theπ-resonance and hydrogen bonding interactions.This concept has been well-accepted in academia and is widely used in practice.However,it has been argued that the seemingly enhanced intramolecular hydrogen bonding(IMHB)in unsaturated compounds may simply be a result of the constraints imposed by theσ-skeleton framework.Thus,it is crucial to estimate the strength of IMHBs.In this work,we used two approaches to probe the resonance effect and estimate the strength of the IMHBs in the two exemplary cases of the enol forms of acetylacetone and o-hydroxyacetophenone.One approach is the block-localized wavefunction(BLW)method,which is a variant of the ab initio valence bond(VB)theory.Using this approach,it is possible to derive the geometries and energetics with resonance shut down.The other approach is Edmiston’s truncated localized molecular orbital(TLMO)technique,which monitors the energy changes by removing the delocalization tails from localized molecular orbitals.The integrated BLW and TLMO studies confirmed that the hydrogen bonding in these two molecules is indeed enhanced byπ-resonance,and that this enhancement is not a result ofσconstraints.

Energy levels and states of parabolic cylindrical lens shaped quantum dots

The parabolic cylindrical lens shaped quantum dot is investigated theoretically. The Schrǒdinger equation for an electron confined in this structure is solved in the parabolic cylindrical coordinate system. The wavefunctions for the electron are presented in terms of confluent hypergeometric functions, and the electron energy spectra are also obtained.

Magneto-optical properties of self-assembled InAs quantum dots for quantum information processing

Semiconductor quantum dots have been intensively investigated because of their fundamental role in solid-state quan- tum information processing. The energy levels of quantum dots are quantized and can be tuned by external field such as optical, electric, and magnetic field. In this review, we focus on the development of magneto-optical properties of single InAs quantum dots embedded in GaAs matrix, including charge injection, relaxation, tunneling, wavefunction distribution, and coupling between different dimensional materials. Finally, the perspective of coherent manipulation of quantum state of single self-assembled quantum dots by photocurrent spectroscopy with an applied magnetic field is discussed.

Incoherent control of two classes of finite-level quantum systems

The incoherent control of finite-level quantum systems is investigated. Following a brief introduction to coherent control paradigms in quantum control, a control problem that can not be accomplished using only coherent control is presented. For such a control problem, it is proved that it can be accomplished using incoherent control based on projective measurement and coherent control for two classes of finite-level quantum systems, i.e., eigenstate controllable quantum systems and wavefunction controllable quantum systems.

Hidden Anderson localization in disorder-free Ising–Kondo lattice

Anderson localization (AL) phenomena usually exist in systems with random potential. However, disorder-free quantum many-body systems with local conservation can also exhibit AL or even many-body localization transition. We show that the AL phase exists in a modified Kondo lattice without external random potential. The density of state, inverse participation ratio and temperature-dependent resistance are computed by classical Monte Carlo simulation, which uncovers an AL phase from the previously studied Fermi liquid and Mott insulator regimes. The occurrence of AL roots from quenched disorder formed by conservative localized moments. Interestingly, a many-body wavefunction is found, which captures elements in all three paramagnetic phases and is used to compute their quantum entanglement. In light of these findings, we expect that the disorder-free AL phenomena can exist in generic translation-invariant quantum many-body systems.

The impact of vibrational wave function on low energy electron vibrational scattering from nitrogen molecule

The vibrational wave function of the target theoretically plays an important role in the calculation of vibrational excitation cross sections. By a careful study of the differential cross sections resulting from different vibrational wave functions we find that cross sections are susceptible to vibrational wave functions. Minor changes in the vibration wave lhnction may cause a significant change in the cross section. Even more surprising is that by selecting a few numbers of potential models （which determine the vibrational wave functions） we can often calculate the differential scattering cross section in much closer agreement with experiment in the framework of body-frame vibrational close-coupling theory, which suggest that an accurate potential energy may play a more important role in scattering than we thought betbre.

A New Form for the Full Salpeter Equation

A more general form of the Bethe Salpater wavefunction for a quark antiquark bound state, in accordance with the spirit of nonrelativistic approximation, is constructed, and the relativistic Salpeter equation is reduced to two 2×2 matrix equations under an instantaneous approximation, which includes not only the contributions comming from a positive energy state but also ones of a negative energy state, and has no anomalous solution.

Analytical Study of Band Structure of Material Using Relativistic Concept

In this paper, we present the study of band structure relativistically. Here, Dirac equation is formulated from Hamilto-nian in which the formulation is found to contain a correction term known as spin-orbit coupling given as that modifies the non-relativistic expression for the same formulation. This term leads to double spin-degeneracy within the first Brillioun zone which is a concept that is not found in other method of study of band structure of material.

Investigating Initial Conditions of the WdW Equation in Flat Space in a Transition from the Pre-Planckian Physics Era to the Electroweak Regime of Space-Time

This document is due to reviewing an article by Maydanyuk and Olkhovsky, of a Nova Science conpendium as of “The big bang, theory assumptions and Problems”, as of 2012, which uses the Wheeler De Witt equation as an evolution equation assuming a closed universe. Having the value of k, not as the closed universe, but nearly zero of a nearly flat universe, which leads to serious problems of interpretation of what initial conditions are. These problems of interpretations of initial conditions tie in with difficulties in using QM as an initial driver of inflation. And argue in favor of using a different procedure as far as forming a wave function of the universe initially. The author wishes to thank Abhay Ashtekar for his well thought out criticism but asserts that limitations in space-time geometry largely due to when is formed from semi classical reasoning, i.e. Maxwell’s equation involving a close boundary value regime between Octonionic geometry and flat space non Octonionic geometry is a datum which Abhay Ashekhar may wish to consider in his quantum bounce model and in loop quantum gravity in the future.

Wrong Potential Energy Term in Schrödinger’s Equation for Hydrogen Atom

Even after nine decades of successful run of the Quantum Mechanics (QM), different viewpoints on foundational problems of Quantum Physics are still being actively debated. That is because mathematical logic of QM often defies the physical intuition which constitutes the main spirit of Physics. De Broglie’s hypothesis of matter waves implied that the dynamic characteristics of a micro particle in motion, can be ascribed to the wave characteristics of the wavelet accompanying the particle. The Schrödinger equation models the matter-wave interactions through wavefunction ψ?and effectively serves as the foundation of QM. Even though mathematical structure of the Schrödinger equation is sound and elegant, here we show a conceptual mistake in the development of this equation wherein the physical situation has not been correctly modeled in the equation. The Coulomb potential energy of the proton electron pair in Hydrogen atom is essentially the negative interaction energy between their superposed electrostatic fields which is inversely proportional to their instantaneous separation distance. Assuming the proton to be relatively fixed at the origin of an appropriate coordinate system, the potential energy of the orbiting electron will be a function of instantaneous position coordinates of the electron. This has not been properly modeled in the Schrödinger equation. The resulting errors in the solution have been quantitatively demonstrated in this paper. We have stressed the necessity of incorporating a specific correction in the potential energy term of the Schrödinger equation, after which it may facilitate the adoption of Bohmian QM.

A New Interpretation of Quantum Mechanics

The Copenhagen interpretation is the most authorized interpretation of quantum mechanics, but there are a number of ideas that are associated with the Copenhagen interpretation. It is ceratin that this fact is not necessarily desirable. Thus, we propose a new interpretation of measurement theory, which is the linguistic aspect (or, the mathematical generalization) of quantum mechanics. Although this interpretation is superficially similar to a part of so-called Copenhagen interpretation, we show that it has a merit to be applicable to both quantum and classical systems. For example, we say that Bell’s inequality is broken even in classical systems.

Dyeing Thermodynamics and Supramolecular Structure of Lac Red on Protein Fibers

The dyeing temperature of natural dye lac red on two kinds of natural protein fibers was studied, and the interaction between dyestuff and fiber was discussed through thermodynamic study and density functional theory (DFT) calculation. The optimum temperature for lac red dyed silk was 60˚C and wool showed a better response at 90˚C. The thermodynamics study revealed good Nernst isotherm and Freundlich adsorption models respectively, and the lac dye adsorption processes were both spontaneous and exothermic. The potential interaction of Laccaic acid A with the external environment by electrostatic potential and atomic charge distribution was first explored. With molecular simulation, Laccaic acid A and glycine composed 8 stable complexes. Then, typical hydrogen bonds, bond length, and binding energy, etc. were analyzed. The results revealed lac red on silk and wool fabric mainly depended on the weak hydrogen bonds and van der Waals force which determined the low dye fastness.

Small Components of the Wave Function of Electron

This paper shows that the moving or time-varying large components of four-component wavefunction of electron would induce small components, and vice versa. Then when a wave packet of electron is moving with high speeds or varies rapidly, or its size is sufficiently small, or in the presence of a strong electromagnetic field, its small components and the related effects cannot be ignored. Furthermore, the spin quantum states of both a moving electron and a motionless electron can be affected by some special electrostatic fields. This may open a new pathway for spintronics to the manipulation of electron spins in the absence of applied magnetic fields.