Non-relativistic Quantum Dynamics Research Articles

Derivation of the Schrödinger equation from QED

The Schrödinger equation relates the emergent quantities of wavefunction and electric potential and is postulated as a principle of quantum physics or obtained heuristically. However, physical consistency requires that the Schrödinger equation is a low-energy dynamical condition we can derive from the foundations of quantum electrodynamics. Due to the small value of the electromagnetic coupling constant, we show that the electric potential accurately represents the contributions of intermediate low-energy photon exchanges. Then, from the total nonrelativistic energy relation, we see that the dominant term of the electron wavefunction is a superposition of plane waves that satisfies the Schrödinger equation. Our derivation shows that the Schrödinger equation is not an energy conservation relation because its middle term does not represent the electron kinetic energy as assumed. We analyze the physical content of the Schrödinger equation and verify our assessments by calculating and evaluating the physical quantities in the ground state of the hydrogen atom. Furthermore, we explain why nonrelativistic quantum dynamics differs from classical dynamics. Undergraduate students can follow the derivation because it involves fundamental physical concepts and mathematical expressions, and we explain every step.

Non-relativistic quantum dynamics in Born–Infeld gravity inspired by Eddington spacetime global monopole

In this work, we investigate the quantum dynamics of non-relativistic systems in a Born–Infeld spacetime. We analyze some general scenarios, which concerns the effects of a harmonic oscillator and an inverse square-type potential as well as an Aharonov–Bohm geometric phase. We obtain an analytical solution for the most general case in terms of a confluent Heun function and define the energy spectrum by referring to the ground state, together with its respective eigenfunction. A graphical representation was built so that it was possible to visualize some of the possible energy configurations. For negative values of the Born–Infeld parameter [Formula: see text], we perform a connection with results of quantum dynamics already investigated in the literature for the Ellis–Bronnikov spacetime.

Epistemic Uncertainty from an Averaged Hamilton–Jacobi Formalism

In recent years, the non-relativistic quantum dynamics derived from three assumptions; (i) probability current conservation, (ii) average energy conservation, and (iii) an epistemic momentum uncertainty (Budiyono and Rohrlich in Nat Commun 8:1306, 2017). Here we show that, these assumptions can be derived from a natural extension of classical statistical mechanics.

The relativistic Aharonov–Bohm–Coulomb system with position-dependent mass

In this work, we study the influence of the Aharonov–Bohm–Coulomb (ABC) system on the relativistic and non-relativistic quantum dynamics of a charged Dirac particle with position-dependent mass (PDM). In order to solve exactly our system, we use both the left-handed and right-handed projection operators. Next, we determine the Dirac spinor and the relativistic energy spectrum, where we observe that this spinor is written in terms of the generalized Laguerre polynomials and this spectrum depends explicitly on the quantum numbers n and ml, parameters Z and that characterize the ABC system, and on the parameter that characterizes the PDM. In particular, we analyse the behavior of the energies as a function of for different values of Z. Finally, we consider the non-relativistic limit and we compared our problem with others works in the literature, where we verify that our results turn out to generalize some particular cases.

Disagreement between non-relativistic and relativistic quantum dynamics of a driven electron

We show, both analytically and numerically, that the non-relativistic and relativistic quantum predictions for the dynamics of a prototypical driven electron – the periodically kicked rotor – do not always agree in the non-relativistic regime. The surprisingly different quantum predictions could be tested experimentally using ultra-cold fermionic atoms in a periodically-pulsed 1D optical lattice. Similar breakdown of agreement should occur for driven quantum systems in general. Since the relativistic theory should be empirically correct, it must be used instead of the approximate non-relativistic theory to correctly study the quantum dynamics of a driven system after the breakdown time, which could lead to important contributions in a wide range of fields from atomic to molecular, chemical and condensed-matter physics.

Quantum dynamics of Bose-Fermi mixtures via the stochastic-wave-function approach

We present a reformulation of the nonrelativistic many-body quantum dynamics of Bose-Fermi mixtures via stochastic wave functions. We show that, within a wide range of two-particle interactions and a certain class of greater-than-two-particle interactions, the quantum dynamics can be mapped exactly onto a set of single-particle wave functions, with their evolution governed by a stochastic process.

Detecting axions via induced electron spin precession

We propose a new window to detect axion-like particle (ALP) dark matter from electrically charged fermions, such as electrons and quarks. We specifically consider a direct interaction between the axion and the electron and find that the non-relativistic quantum dynamics induces a spin precession due to the axion and is enhanced by the application of an external electric field. This precession gives a change in magnetic flux which under certain circumstances can yield a detectable signal for SQUID magnetometers.

Quantum states of a neutral massive fermion with an anomalous magnetic moment in an Aharonov–Casher field

The planar nonrelativistic quantum dynamics of a neutral massive fermion with an anomalous magnetic moment (AMM) in the electric field of infinitely long and thin thread with a charge density distributed uniformly along it (an Aharonov–Casher field) is examined. The relevant Hamiltonian is singular and requires additional specification of a one-parameter self-adjoint extension, which can be given in terms of physically acceptable boundary conditions. We find all possible self-adjoint Hamiltonians with an Aharonov–Casher field (ACF) by constructing the corresponding Hilbert space of square-integrable functions, including the [Formula: see text] region, for all their Hamiltonians. We determine the most relevant physical quantities, such as energy spectrum and wave functions and discuss their correspondence with those obtained by the physical regularization procedure. We show that energy levels of bound states are simple poles of the scattering amplitude. It is shown that the scattering amplitudes and cross-sections depend essentially on the initial-state spin of fermions.

Quantum Phase for an Electric Multipole Moment in Noncommutative Quantum Mechanics

We study the noncommutative nonrelativistic quantum dynamics of a neutral particle, which possesses an electric multipole moment, in the presence of an external magnetic field. First, by introducing a shift for the magnetic field we give the Schrodinger equations in the presence of an external magnetic field both on a noncommutative space and a noncommutative phase space, respectively. Then by solving the Schrodinger equations, we obtain quantum phases of the electric multipole moment both on a noncommutative space and a noncommutative phase space. We demonstrate that these phase are geometric and dispersive.

Quantum motion of a point particle in the presence of the Aharonov–Bohm potential in curved space

The nonrelativistic quantum dynamics of a spinless charged particle in the presence of the Aharonov–Bohm potential in curved space is considered. We chose the surface as being a cone defined by a line element in polar coordinates. The geometry of this line element establishes that the motion of the particle can occur on the surface of a cone or an anti-cone. As a consequence of the nontrivial topology of the cone and also because of two-dimensional confinement, the geometric potential should be taken into account. At first, we establish the conditions for the particle describing a circular path in such a context. Because of the presence of the geometric potential, which contains a singular term, we use the self-adjoint extension method in order to describe the dynamics in all space including the singularity. Expressions are obtained for the bound state energies and wave functions.

Geometric phases modified by a Lorentz-symmetry violation background

We analyze the nonrelativistic quantum dynamics of a single neutral spin-half particle, with nonzero magnetic and electric dipole moments, moving in an external electromagnetic field in the presence of a Lorentz-symmetry violating background. We also study the geometric phase for this model taking in account the influence of the parameter that breaks the Lorentz-symmetry. These geometric phases are used to impose an upper bound on the background magnitude.

Geometric quantum phases from Lorentz symmetry breaking effects in the cosmic string spacetime

By starting from the modified Maxwell theory coupled to gravity, the arising of geometric quantum phases in the relativistic and nonrelativistic quantum dynamics of a Dirac neutral particle from the effects of the violation of the Lorentz symmetry in the cosmic string spacetime is investigated. It is shown that the Dirac equation can be written in terms of an effective metric and a relativistic geometric phase stems from the topology of the cosmic string spacetime and the Lorentz symmetry breaking effects. Further, the nonrelativistic limit of the Dirac equation is discussed and it is shown that both Lorentz symmetry breaking effects and the topology of the defect yields a phase shift in the wave function of the nonrelativistic spin-1/2 particle.

On the Lorentz symmetry breaking effects on a Dirac neutral particle inside a two-dimensional quantum ring

We study the effects of the Lorentz symmetry violation in the nonrelativistic quantum dynamics of a spin-1/2 neutral particle interacting with external fields confined to a two-dimensional quantum ring (W.-C. Tan, J.C. Inkson, Semicond. Sci. Technol. 11, 1635 (1996)). We show a possible scenario for the Lorentz symmetry breaking that permits us to make an analogy with the Landau-Aharonov-Casher system (M. Ericsson, E. Sjoqvist, Phys. Rev. A 65, 013607 (2001)), where a change in the angular frequency characteristic of the confinement of a quantum particle to a two-dimensional ring is obtained. Then, we show that an upper bound for the Lorentz symmetry breaking parameters may be set up. Besides, we analyse another possible scenario of the Lorentz symmetry violation by showing the presence of an analogue of the Coulomb potential. We obtain the bound states solutions to the Schrodinger-Pauli equation and discuss a quantum effect characterized by the dependence of the angular frequency on the quantum numbers of the system.

Quantum phase for an electric quadrupole moment in noncommutative quantum mechanics

We study the noncommutative nonrelativistic quantum dynamics of a neutral particle, which possesses an electric qaudrupole moment, in the presence of an external magnetic field. First, by introducing a shift for the magnetic field, we give the Schrodinger equations in the presence of an external magnetic field both on a noncommutative space and a noncommutative phase space, respectively. Then by solving the Schrodinger equations both on a noncommutative space and a noncommutative phase space, we obtain quantum phases of the electric quadrupole moment, respectively. We demonstrate that these phases are geometric and dispersive.

Geometric approach to non-relativistic quantum dynamics of mixed states

In this paper we propose a geometrization of the non-relativistic quantum mechanics for mixed states. Our geometric approach makes use of the Uhlmann's principal fibre bundle to describe the space of mixed states and as a novelty tool, to define a dynamic-dependent metric tensor on the principal manifold, such that the projection of the geodesic flow to the base manifold gives the temporal evolution predicted by the von Neumann equation. Using that approach we can describe every conserved quantum observable as a Killing vector field, and provide a geometric proof for the Poincaré quantum recurrence in a physical system with finite energy levels.

Abelian geometric phase due to the presence of an edge dislocation

We study the appearance of an Abelian geometric phase in relativistic and nonrelativistic quantum dynamics of a neutral particle due to the presence of an edge dislocation. We demonstrate that the nonminimal coupling of fermions with torsion introduces a geometric phase in the wave function of the neutral particle in relativistic and in nonrelativistic quantum dynamics.

Nonrelativistic quantum dynamics on a cone with and without a constraining potential

In this paper we investigate the bound state problem of nonrelativistic quantum particles on a conical surface. This kind of surface appears as a topological defect in ordinary semiconductors as well as in graphene sheets. Specifically, we compare and discuss the results stemming from two different approaches. In the first one, it is assumed that the charge carriers are bound to the surface by a constraining potential, while the second one is based on the Klein-Gordon type equation on surfaces, without the constraining potential. The main difference between both theories is the presence/absence of a potential which contains the mean curvature of a given surface. This fact changes the dependence of the bound states on the angular momentum l. Moreover, there are bound states that are absent in the Klein-Gordon theory, which instead appear in the Schrödinger one.

LANDAU QUANTIZATION FOR A NEUTRAL PARTICLE IN THE PRESENCE OF TOPOLOGICAL DEFECTS

In this short communication, we study the Landau levels in the non-relativistic quantum dynamics of a neutral particle which possesses a permanent magnetic dipole moment interacting with an external electric field in curved spacetime background with the presence or absence of a torsion field. We show that the presence of the topological defect breaks the infinite degeneracy of the Landau levels.

Trajectory-based solution of the nonadiabatic quantum dynamics equations: an on-the-fly approach for molecular dynamics simulations

The non-relativistic quantum dynamics of nuclei and electrons is solved within the framework of quantum hydrodynamics using the adiabatic representation of the electronic states. An on-the-fly trajectory-based nonadiabatic molecular dynamics algorithm is derived, which is also able to capture nuclear quantum effects that are missing in the traditional trajectory surface hopping approach based on the independent trajectory approximation. The use of correlated trajectories produces quantum dynamics, which is in principle exact and computationally very efficient. The method is first tested on a series of model potentials and then applied to study the molecular collision of H with H(2) using on-the-fly TDDFT potential energy surfaces and nonadiabatic coupling vectors.

Anandan quantum phase for a neutral particle with Fermi–Walker reference frame in the cosmic string background

We study geometric quantum phases in the relativistic and non-relativistic quantum dynamics of a neutral particle with a permanent magnetic dipole moment interacting with two distinct field configurations in a cosmic string spacetime. We consider the local reference frames of the observers are transported via Fermi–Walker transport and study the influence of the non-inertial effects on the phase shift of the wave function of the neutral particle due to the choice of this local frame. We show that the wave function of the neutral particle acquires non-dispersive relativistic and non-relativistic quantum geometric phases due to the topology of the spacetime, the interaction between the magnetic dipole moment with external fields and the spin–rotation coupling. However, due to the Fermi–Walker reference frame, no phase shift associated to the Sagnac effect appears in the quantum dynamics of a neutral particle. We show that in the absence of topological defect, the contribution to the quantum phase due to the spin–rotation coupling is equivalent to the Mashhoon effect in non-relativistic dynamics.