The Aharonov-Bohm Effect: An Exploration of Quantum Interference and Electromagnetic Potentials

The AB(Aharonov-Bohm)effect is a pivotal quantum mechanical phenomenon that illustrates the fundamental role of the electromagnetic vector potential A in determining the phase of a charged particle’s wave function,even in regions where the magnetic field B is zero.This effect demonstrates that quantum particles are influenced not only by the fields directly present but also by the potentials associated with those fields.In the AB effect,an electron beam is split into two paths,with one path encircling a solenoid and the other bypassing it.Despite the absence of a magnetic field in the regions traversed by the beams,the vector potential A associated with the magnetic flux Φ through the solenoid induces a phase shift in the electron’s wave function.This phase shift,quantified by △φ=qΦ/hc,manifests as a change in the interference pattern observed in the detection screen.The phenomenon underscores the principle of gauge invariance in QED(quantum electrodynamics),where physical observables remain invariant under local gauge transformations of the vector and scalar potentials.This reinforces the notion that the vector potential A has a profound impact on quantum systems,beyond its classical role.This article outlines the AB effect,including its theoretical framework,experimental observations,and implications.The focus on the role of the vector potential in quantum mechanics provides a comprehensive understanding of this important phenomenon.

The decoherence of the triangular and Coulomb bound potential quantum dot qubit

We study the eigenenergies and eigenfunctions of the ground and first-excited states of an electron which is strongly coupled to an LO-phonon in a quantum dot with a triangular bound potential and Coulomb bound potential by using the Pekar variational method. This system may be used as a two-level qnbit. Phonon spontaneous emission causes the decoherence of the qubit. Numerical calculations are performed on the decoherence rate as a function of the polar angle, the Coulomb binding parameter, the coupling strength, the confinement length of the quantum dot and the dispersion coefficient.

Quantum information entropies of the eigenstates for the Pschl-Teller-like potential

Shannon entropy for lower position and momentum eigenstates of Ptschl-Teller-like potential is evaluated. Based on the entropy densities demonstrated graphically, we note that the wave through of the position information entropy density p （x） moves right when the potential parameter V1 increases and its amplitude decreases. However, its wave through moves left with the increase in the potential parameter 丨V2丨. Concerning the momentum information entropy density p（p）, we observe that its amplitude increases with increasing potential parameter V1, but its amplitude decreases with increasing丨V2丨. The Bialynicki-Birula-Mycielski （BBM） inequality has also been tested for a number of states. Moreover, there exist eigenstates that exhibit squeezing in the momentum information entropy. Finally, we note that position information entropy increases with V1, but decreases with 丨V2丨, However, the variation of momentum information entropy is contrary to that of the position information entropy.

The energy-level and vibrational frequency properties of a polaron weak-coupled in a quantum well with asymmetrical Gaussian confinement potential

The vibrational frequency(VF), the ground state(GS) energy and the GS binding energy of the weak electron-phonon coupling polaron in a quantum well(QW) with asymmetrical Gaussian confinement potential are calculated. First we introduce the linear combination operator to express the momentum and coordinates in the Hamilton and then operate the system Hamilton using unitary transformation. The results indicate the relations of the quantities(the VF, the absolute value of GS energy and the GS binding energy) and the parameters(the QW barrier height and the range of Gaussian confinement potential in the growth direction of the QW).

Effects of Thermal Lattice Vibration on the Effective Potential of Weak-Coupling Bipolaron in a Quantum Dot

Based on the Huybrechts' linear-combination operator,effects of thermal lattice vibration on the effective potential of weak-coupling bipolaron in semiconductor quantum dots are studied by using the LLP variational method and quantum statistical theory.The results show that the absolute value of the induced potential of the bipolaron increases with increasing the electron-phonon coupling strength,but decreases with increasing the temperature and the distance of electrons,respectively;the absolute value of the effective potential increases with increasing the radius of the quantum dot,electron-phonon coupling strength and the distance of electrons,respectively,but decreases with increasing the temperature;the temperature and electron-phonon interaction have the important influence on the formation and state properties of the bipolaron:the bipolarons in the bound state are closer and more stable when the electron-phonon coupling strength is larger or the temperature is lower;the confinement potential and coulomb repulsive potential between electrons are unfavorable to the formation of bipolarons in the bound state.

Graphene Quantum Wells and Superlattices Driven by Periodic Linear Potential

The transfer matrices for both nonsingular and singular cases are constructed to ensure efficient and accurate numerical computation on the electronic and transport properties of graphene quantum wells and superlattices driven by periodic linear potential.An intuitive interpretation is given for the evolution behavior of the current flowing through the multiple graphene quantum wells/barriers by analyzing the interrelationship among the transmission,bias voltage,incident velocity,and linear potential ranges.The energy minibands and density of states of the graphene superlattices with different periods are also examined by using analytical and numerical methods,showing that the period of superlattices plays a crucial role in energy bands and density of states.

Temperature Effects of Parabolic Linear Bound Potential and Coulomb Bound Potential Quantum Dot Qubit

On the condition of electric-LO phonon strong coupling in a parabolic quantum dot,we obtain theeigenenergy and the eigenfunctions of the ground state and the first-excited state using the variational method ofPekar type.This system in a quantum dot may be employed as a two-level quantum system-qubit.When the electronis in the superposition state of the ground state and the first-excited state,we obtain the time evolution of the electrondensity.The relations of the probability density of electron on the temperature and the electron-LO-phonon couplingconstant and the relations of the period of oscillation on the temperature,the electron-LO-phonon coupling constant,the Coulomb binding parameter and the confinement length are derived.The results show that the probability densityof electron oscillates with a period when the electron is in the superposition state of the ground and the first-excitedstate,and show that there are different laws that the probability density of electron and the period of oscillation changewith the temperature and the electron-LO-phonon coupling constant when the temperature is lower or higher.Andit is obtained that the period of oscillation decreases with increasing the Coulomb bound potential and increases withincreasing the confinement length not only at lower temperatures but also at higher temperatures.

Ionization Potentials and Quantum Defects of 1s^2np^2p Rydberg States of Lithium Atom

Abstract In this work, ionization potentials and quantum effects of ls^2 np^2 P Rydberg states of lithium are calculated based on the calibrated quantum defect function. Energy levels and quantum defects for ls^2np^2P bound states and their adjacent continuum states are calculated with the R-matrix theory, and then the quantum defect function of the ls^2np （n ≥ 7） channel is obtained, which varies smoothly with the energy based on the quantum defect theory. The accurate quantum defect of the ls^2 7p^2P state derived from the experimental data is used to calibrate the original quantum defect function. The new function is used to calculate ionization potentials and quantum effects of ls^2np ^2P （n ≥ 7） Rydberg states. Present calculations are in agreement with recent experimental data in whole.

Quantum Mechanical Hilbert Transformation for Normally Ordering Coulomb Potential-Type Operators

We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by using the mathematical Hilbert transform formula.

Calculation of Quantum Probability in O（2,2） String Cosmology with a Dilaton Potential

The quantum properties of O（2,2） string cosmology with a dilaton potential are studied in this paper. The cosmological solutions are obtained on three-dlmensional space-time. Moreover, the quantum probability of transition between two duality universe is calculated through a Wheeler-De Witt approach.

Pseudospin symmetric solutions of the Dirac equation with the modified Rosen-Morse potential using Nikiforov-Uvarov method and supersymmetric quantum mechanics approach

Employing the Pekeris-type approximation to deal with the pseudo-centrifugal term,we analytically study the pseudospin symmetry of a Dirac nucleon subjected to equal scalar and vector modified Rosen-Morse potential including the spin-orbit coupling term by using the Nikiforov-Uvarov method and supersymmetric quantum mechanics approach.The complex eigenvalue equation and the total normalized wave functions expressed in terms of Jacobi polynomial with arbitrary spin-orbit coupling quantum number k are presented under the condition of pseudospin symmetry.The eigenvalue equations for both methods reproduce the same result to affirm the mathematical accuracy of analytical calculations.The numerical solutions obtained for different adjustable parameters produce degeneracies for some quantum number.

Quantum Standing Waves and Tunneling Through a Finite Range Potential

We consider a time independent one dimensional finite range and repulsive constant potential barrier between two impenetrable walls. For a nonrelativistic massive particle projected towards the potential with energies less than the barrier and irrespective of the spatial positioning of the potential allowing for quantum tunneling, analytically we solve the corresponding Schrodinger equation. For a set of suitable parameters utilizing Mathematica we display the wave functions along with their associated probabilities for the entire region. We investigate the sensitivity of the probability distributions as a function of the potential range and display a gallery of our analysis. We extend our analysis for bound state particles confined within constant attractive potentials.

Spin Supercurrent in Phenomena of Quantum Non-Locality (Quantum Correlations, Magnetic Vector Potential) and in Near-Field Antenna Effect

It is shown that such phenomena as quantum correlations (interaction of space-separated quantum entities), the action of magnetic vector potential on quantum entities in the absence of magnetic field, and near-field antenna effect (the existence of superluminally propagating electromagnetic fields) may be explained by action of spin supercurrents. In case of quantum correlations between quantum entities, spin supercurrent emerges between virtual particles pairs (virtual photons) created by those quantum entities. The explanation of magnetic vector potential and near-field antenna effect is based on contemporary principle of quantum mechanics: the physical vacuum is not an empty space but the ground state of the field consisting of quantum harmonic oscillators (QHOs) characterized by zero-point energy. Using the properties of the oscillators and spin supercurrent, it is proved that magnetic vector potential is proportional to the moment causing the orientation of spin of QHO along the direction of magnetic field. The near-field antenna effect is supposed to take place as a result of action of spin supercurrent causing secondary electromagnetic oscillations. In this way, the electromagnetic field may spread at the speed of spin supercurrent. As spin supercurrent is an inertia free process, its speed may be greater than that of light, which does not contradict postulates of special relativity that sets limits to the speed of inertial systems only.

Nature of the Quantum Potential

In this paper we suggested a natural interpretation of the de Broglie-Bohm quantum potential, as the energy due to the oscillating electromagnetic field (virtual photon) coupled with moving charged particle. Generalization of the Schr&oumldinger equation is obtained. The wave function is shown to be the eigenfunction of the Sturm-Liouville problem in which we expand virtual photon to include it implicitly into consideration. It is shown that the non-locality of quantum mechanics is related only with virtual photon. As an example, the zero-energy of harmonic oscillator is obtained from classical equations.

Localization and recurrence of a quantum walk in a periodic potential on a line

We present a numerical study of a model of quantum walk in a periodic potential on a line. We take the simple view that different potentials have different affects on the way in which the coin state of the walker is changed. For simplicity and definiteness, we assume that the walker＇s coin state is unaffected at sites without the potential, and rotated in an unbiased way according to the Hadamard matrix at sites with the potential. This is the simplest and most natural model of a quantum walk in a periodic potential with two coins. Six generic cases of such quantum walks are studied numerically. It is found that, of the six cases, four cases display significant localization effect where the walker is confined in the neighborhood of the origin for a sufficiently long time. Associated with such a localization effect is the recurrence of the probability of the walker returning to the neighborhood of the origin.

Exact solution of Schrdinger equation with q-deformed quantum potentials using Nikiforov–Uvarov method

In this paper, we present the exact solution of the one-dimensional Schrrdinger equation for the q-deformed quantum potentials via the Nikiforov-Uvarov method. The eigenvalues and eigenfunctions of these potentials are obtained via this method. The energy equations and the corresponding wave functions for some special cases of these potentials are briefly discussed. The PT-symmetry and Hermiticity for these potentials are also discussed.

Self-optimizing Diffusion Quantum Monte Carlo Calculation: the Potential Energy Curve of C_2

In this paper we propose a novel diffusion quantum Monte Carlo algo-rithm, it is a self-optimizing and self-improving procedure. The method has been em-ployed to calculate the potential energy curve of C2. The total energies for the X 1Σg+state of C2 were calculated at seven values of the bond length: 0. 106, 0. 111, 0. 124,0. 132, 0. 143, 0. 159 and 0. 185 nm; and a smooth potential energy curve was ob-tained, because when the self-optimizing technique is used, the statistical error decreas-es tremendously. The calculation results on the potential energy curve of C2 show thatthe self-optimizing diffusion quantum Monte Carlo method proposed in the present pa-per is successful.

The Yukawa potential in semirelativistic formulation via supersymmetry quantum mechanics

We apply an approximation to the centrifugal term and solve the two-body spinless-Salpeter equation （SSE） with the Yukawa potential via the supersymmetric quantum mechanics （SUSYQM） for arbitrary quantum numbers. Useful figures and tables are also included.

Binding energy of the donor impurities in GaAs-Ga_(1-x)Al_xAs quantum well wires with Morse potential in the presence of electric and magnetic fields

The behavior of a donor in the GaAs–GaAlAs quantum well wire represented by the Morse potential is examined within the framework of the effective-mass approximation. The donor binding energies are numerically calculated for with and without the electric and magnetic fields in order to show their influence on the binding energies. Moreover, how the donor binding energies change for the constant potential parameters(De, re, and a) as well as with the different values of the electric and magnetic field strengths is determined. It is found that the donor binding energy is highly dependent on the external electric and magnetic fields as well as parameters of the Morse potential.

Effect of Bohm quantum potential in the propagation of ion–acoustic waves in degenerate plasmas

A theoretical investigation has been carried out on the propagation of the ion–acoustic(IA) waves in a relativistic degenerate plasma containing relativistic degenerate electron and positron fluids in the presence of inertial non-relativistic light ion fluid. The Korteweg-de Vries(K-dV), modified K-dV(m K-dV), and mixed m K-dV(mm K-dV) equations are derived by adopting the reductive perturbation method. In order to analyze the basic features(phase speed, amplitude, width,etc.) of the IA solitary waves(SWs), the SWs solutions of the K-dV, m K-dV, and mm K-d V are numerically analyzed. It is found that the degenerate pressure, inclusion of the new phenomena like the Fermi temperatures and quantum mechanical effects(arising due to the quantum diffraction) of both electrons and positrons, number densities, etc., of the plasma species remarkably change the basic characteristics of the IA SWs which are found to be formed either with positive or negative potential. The implication of our results in explaining different nonlinear phenomena in astrophysical compact objects, e.g.,white dwarfs, neutron stars, etc., and laboratory plasmas like intense laser–solid matter interaction experiments, etc., are mentioned.