Narrow Results

Valence electron and positron charge densities in SiC are obtained from wave functions derived in a model pseudopotential bandstructure calculation. It is observed that the positron density is maximum in the open interstices and is excluded not only from the ion cores but also, to a considerable degree, from the valence bonds. Electron–positron momentum densities are calculated for the (001–110) plane. The results are used to analyze the positron effect in large gap semiconductors.

A method is proposed to find the wave function of an electron moving infinitely in the field of an arbitrary 1D layered structure with two different homogeneous semi-infinite boundaries. It is shown that in general the problem reduces to solution of a set of two linear recurrent equations. The proposed approach is discussed on a base of two cases: a structure of periodically placed identical rectangular potentials and a nonordered structure with certain distortion of periodicity and potential identity.

We examine the imbalance thermodynamics of uncontaminated decoherence in graphene. In a uncontaminated decoherence process, no exchange of energy takes place directly between graphene and the surroundings. It is seen that due to decoherence heat dissolution takes place due to which energy of the environment cannot remain conserved. In this paper, we find out the energy eigenvalues and wave function in the graphene from the perturbed Hamiltonian to find out the density matrix and entropy of the system and their unique relation between the density matrix, momentum of the graphene and entropy where the graphene is taken as an open system. In graphene, the behavior of electrons is controlled by the massless Hamiltonian and ($2+1$) Dirac equation.

Using Mathematica 3.0, the Schrödinger equation for bound states is solved. The method of solution is based on a numerical integration procedure together with convexity arguments and the nodal theorem for wave functions. The interaction potential has to be spherically symmetric. The solving procedure is simply defined as some Mathematica function. The output is the energy eigenvalue and the reduced wave function, which is provided as an interpolated function (and can thus be used for the calculation of, e.g., moments by using any Mathematica built-in function) as well as plotted automatically. The corresponding program schroedinger.nb can be obtained from franz.schoeberl@univie.ac.at.

We obtain the Schrödinger wave functions of a generalized pendulum under time-dependent gravitation by making use of the Lewis and Riesenfeld invariant method. As an example, we consider a generalized pendulum with constant gravitation and exponentially increasing mass. We also present a canonical approach to the generalized time-dependent pendulum.

By applying a spatially extended sink operator, the nucleon two-point functions are calculated in Coulomb gauge from quenched lattice QCD with overlap fermions. The Bethe-Salpeter wave functions of nucleon and Roper resonance are extracted at different quark masses. The typical size of nucleon is about 0.7 fm, which seems insensitive to the quark masses involved in this work. It is also found that the wave function of Roper has a radial node.

The general form of the Bethe–Salpeter wave functions for bound states comprising one scalar constituent and one fermion, or two scalars is presented. Using the reduced Salpeter equation obtained, we can work out the effective nonrelativistic potentials. And one new version of reduced Bethe–Salpeter equation is proposed by extending Gross approximation.

The eigenvalue equation of the dynamical Schrödinger operator in polar coordinates without potential is considered. An integral transformation in terms of the Bessel's functions is suggested as a solution. The eigenvalue equation is simplified to an ordinary equation in the time variable. The Schrödinger propagator is calculated with the solution of the eigenvalue equation, and used to find explicitly the wave function of the Wheeler–de Witt equation that describes gravity plus a perfect fluid.

In this review, we discuss a relation between quantum communication complexity and a long-standing debate in quantum foundation concerning the interpretation of the quantum state. Is the quantum state a physical element of reality as originally interpreted by Schrödinger? Or is it an abstract mathematical object containing statistical information about the outcome of measurements as interpreted by Born? Although these questions sound philosophical and pointless, they can be made precise in the framework of what we call classical theories of quantum processes, which are a reword of quantum phenomena in the language of classical probability theory. In 2012, Pusey, Barrett and Rudolph (PBR) proved, under an assumption of preparation independence, a theorem supporting the original interpretation of Schrödinger in the classical framework. The PBR theorem has attracted considerable interest revitalizing the debate and motivating other proofs with alternative hypotheses. Recently, we showed that these questions are related to a practical problem in quantum communication complexity, namely, quantifying the minimal amount of classical communication required in the classical simulation of a two-party quantum communication process. In particular, we argued that the statement of the PBR theorem can be proved if the classical communication cost of simulating the communication of n qubits grows more than exponentially in n. Our argument is based on an assumption that we call probability equipartition property. This property is somehow weaker than the preparation independence property used in the PBR theorem, as the former can be justified by the latter and the asymptotic equipartition property of independent stochastic sources. The probability equipartition property is a general and natural hypothesis that can be assumed even if the preparation independence hypothesis is dropped. In this review, we further develop our argument into the form of a theorem.

The coefficients of new analytical forms for the deuteron wave function (DWF) in coordinate space for NijmI, NijmII, Nijm93, Reid93 and Argonne v18 potentials have been numerically calculated. The obtained wave functions do not contain any superfluous knots. The designed parameters of the deuteron are in good agreement with the experimental and theoretical data. The tensor polarization $t_{20}$ calculated based on the wave functions is proportionate to the earlier published results.

The main features of obtaining the asymptotic behavior of the electric structure function $A(p)$ at large values of the transmitted momentum are analyzed. The asymptotic behavior of the structure function $A(p)$ was determined to take into account the asymptotic behavior of the deuteron form factors and the original dipole approximation for the nucleon form factors. Asymptotic values of $A(p)$ were obtained for the nucleon–nucleon potential Reid93 and compared with the calculations for different nucleon form factor models and their approximations. In the broad momentum range up to 12.5 fm${}^{-1}$, the basic forms of the asymptotic behavior of the electric structure function are demonstrated and compared with the experimental data of the modern collaborations. As the analysis shows in most cases considered, the asymptotic for $A(p)$ is represented in the form of the power function $p^{-n}$.

Numerical modeling of the deuteron wave function in the coordinate representation for the phenomenological nucleon–nucleon potential Argonne v18 has been performed. For this purpose, the asymptotic behavior of the radial wave function has been taken into account near the origin of coordinates and at infinity. The charge deuteron form factor $G_C(p)$, depending on the transmitted momentums up to $p=22{\mathrm{\text{fm}}}^{-1}$, has been calculated employing five models for the deuteron wave function. A characteristic difference in calculations of $G_C$ is observed near the positions of the first and second zero. The difference between the obtained values for $G_C$ form factor has been analyzed using the values of the ratios and differences for the results. Obtained outcomes for charge deuteron form factor at large momentums may be a prediction for future experimental data.

The relativistic quantum dynamics of the generalized Klein–Gordon (KG) oscillator having position-dependent mass in the Gödel-type space–time is investigated. We have presented the generalized KG oscillator in this space–time, and discussed the effect of Cornell potential and linear potential for our considered system. The modification from the parameters of position-dependent mass and characterizing the space–time for the energy spectrums are presented.

It is well known that the Klein–Gordon equation in curved spacetime is conformally noninvariant, both with and without a mass term. We show that such a noninvariance provides nontrivial physical insights at different levels, first within the fully relativistic regime, then in the nonrelativistic regime leading to the Schrödinger equation, and then within the de Broglie–Bohm causal interpretation of quantum mechanics. The conformal noninvariance of the Klein–Gordon equation coupled to a vector potential is confronted with the conformal invariance of Maxwell’s equations in the presence of a charged current. The conformal invariance of the nonminimally coupled Klein–Gordon equation to gravity is then examined in light of the conformal invariance of Maxwell’s equations. Finally, the consequence of the noninvariance of the equation on the Aharonov–Bohm effect in curved space–time is discussed.

We derive an expression for the conditional time for the reflection of a wave from an arbitrary potential barrier using the WKB wavefunction in the barrier region. Our result indicates that the conditional times for transmission and reflection are equal for a symmetric barrier within the validity of the WKB approach.

We investigated exact quantum states of the light confined in cubes filled with conductive media whose parameters are explicitly dependent on time and the light propagating under periodic boundary condition by making use of the LR (Lewis–Riesenfeld) invariant operator method. The choice of Coulomb gauge in the charge free space allowed us to evaluate quantized electric and magnetic fields by expanding only the vector potential, since the scalar potential is zero. We also described the fields with a spectrum of continuous mode, which can be obtained by setting the side L to infinity.

A full quantum mechanical treatment of the problem of three electromagnetic fields is considered. The system consists of three different coupling parameters where the rotating and counter-rotating terms are presented. An exact solution of the wave function in the Schrödinger picture is obtained, and the connection to the coherent states wave function is given. The symmetrical ordered quasi-probability distribution function (W-Wigner function) is calculated via the wave function in the coherent states representation. The Green's function is obtained and employed to find the Bloch density matrix. The expectation value of the energy is also given. In the framework of the vacuum and even coherent states, we have discussed the phenomenon of squeezing. It has been shown that the collapse and revival phenomenon exists at ω₁=ω₂ and is apparent for a long period of time.

Using the invariant operator method and the unitary transformation method together, we obtained discrete and continuous solutions of the quantum damped driven harmonic oscillator. The wave function of the underdamped harmonic oscillator is expressed in terms of the Hermite polynomial while that of the overdamped harmonic oscillator is expressed in terms of the parabolic cylinder function. The eigenvalues of the underdamped harmonic oscillator are discrete while that of the critically damped and the overdamped harmonic oscillators are continuous. We derived the exact phases of the wave function for the underdamped, critically damped and overdamped driven harmonic oscillator. They are described in terms of the particular solutions of the classical equation of motion.

The decay process of meta-stable muonic molecules produced in hydrogen isotopes is investigated. J and ν are ro-vibrational quantum numbers. This muonic molecular ion is formed in collisions of excited pμ(2s) atoms with H₂ molecules. Decay of the opens a path for the muon from pμ(2s) to pμ(1s). A scattering-theoretical model, employing a new wave function, is introduced for this process. Variational numerical calculation for decay widths of three low states of is performed using adiabatic representation method.

The quantum states with continuous spectrum for the time-dependent harmonic oscillator perturbed by a singularity are investigated. This system does not oscillate while the system that has discrete energy eigenvalue does. Exact wave functions satisfying the Schrödinger equation for the system are derived using invariant operator and unitary operator together.