Observations of the Ramsauer–Townsend effect in quaternionic quantum mechanics

In this article, one of the well-known effects in quantum mechanics is addressed and also the extended form of quantum mechanics which is based on quaternions is presented. In the presence of this version of quantum mechanics the Ramsauer–Townsend effect has been investigated and the existence of this phenomenon is studied according to quaternionic calculations; results are presented by graphs.     

Nucleon–nucleon scattering in the light of supersymmetric quantum mechanics

By exploiting supersymmetry-inspired factorization method together with a judiciously chosen deuteron ground-state wave function, approximate higher partial wave nucleon–nucleon potentials are generated. In this context, a minor modification is also introduced to the generated potentials. The n–p scattering phase shifts are computed and analysed via the phase function method.     

The revival of Schrödinger's interpretation of quantum mechanics

A distinction is made between two wave functions(x) and(x), The former describing a continuous distribution of electronic matter for a single system, the latter describing the regularities in repeated experiments. The classical field(x) necessarily includes the self energy and accounts for all the radiative processes without the probability interpretation.     

Gauge covariance of the Aharonov–Bohm phase in noncommutative quantum mechanics

The gauge covariance of the wave function phase factor in noncommutative quantum mechanics (NCQM) is discussed. We show that the naive path integral formulation and an approach where one shifts the coordinates of NCQM in the presence of a background vector potential leads to the gauge non-covariance of the phase factor. Due to this fact, the Aharonov–Bohm phase in NCQM which is evaluated through the path-integral or by shifting the coordinates is neither gauge invariant nor gauge covariant. We show that the gauge covariant Aharonov–Bohm effect should be described by using the noncommutative Wilson lines, what is consistent with the noncommutative Schrödinger equation. This approach can ultimately be used for deriving an analogue of the Dirac quantization condition for the magnetic monopole.     

Position measurements in the de Broglie–Bohm interpretation of quantum mechanics

The de Broglie–Bohm interpretation of quantum mechanics assigns positions and trajectories to particles. We analyze the validity of a formula for the velocities of Bohmian particles which makes the analysis of these trajectories particularly simple. We apply it to particle detectors of four different types and show that the detectors of three of these types lead to “surrealistic trajectories”, i.e., leave a trace where the Bohmian particle was not present.     

Critical assessment of the Schrödinger picture of quantum mechanics

We provide an example in which the Heisenberg and the Schrödinger pictures of quantum mechanics give different results, thus confirming the statement of P.A.M. Dirac that the two pictures may lead to inequivalent results. We consider a one-dimensional nonrelativistic charged harmonic oscillator (frequency ω₀ and mass m), and take into account the action of the radiation reaction and the vacuum electromagnetic forces on the charged oscillator. We show that the Heisenberg picture gives the correct value, ℏω₀/2, for the ground state energy of the harmonic oscillator in both cases of classical and quantized vacuum fields. In the case of the Schrödinger picture, considering classical vacuum fields, and using a simple calculation for the classical radiation reaction force that is valid in the limit of large mass (mc²⪢ℏω₀), we obtain the value ℏω₀ for the ground state energy of the harmonic oscillator. We show that the vacuum electromagnetic forces play a very important role in the understanding of this discrepancy.     

The blossoming of quantum mechanics in Italy: the roots,the context and the first spreading in Italian universities (1900–1947)

The European Physical Journal H - The widespread positivist approach of physics research in Italy at the turn of the XIX and XX centuries did not provide a fertile ground for the scientific debate...     

Aφ factory to investigate the foundations of quantum mechanics

A bound on theK oscillating parameter has been obtained by some models of nonlocality. In this paper we stress the fact that aø factory to test the CP-violating parameters in theK system can also probe, through correlated observations of two ⁰, the incompatibility between the quantum mechanics and these formulations of the local realism.     

The Schrödinger group in molecular quantum mechanics: beyond the Born–Oppenheimer approximation

The Galillei transformation invariant form of molecular quantum mechanics is obtained, which is not restricted by the Born–Oppenheimer approximation. The molecular Hamiltonian takes then the form of a linear combination of operators of the Schrödinger group, which define the new space–time molecular symmetry properties (e.g. helicity).

The puzzling homochirality of the hydrogen bonded biomolecular systems appears then as a simple result of the molecular space-time symmetry.     

Logical inference approach to relativistic quantum mechanics: Derivation of the Klein–Gordon equation

The logical inference approach to quantum theory, proposed earlier De Raedt et al. (2014), is considered in a relativistic setting. It is shown that the Klein–Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space–time data collected by probing the particle is obtained from the most robust experiment and that on average, the classical relativistic equation of motion of a particle holds.     

Notes on non-commutative Chern–Simons quantum mechanics

The European Physical Journal C - We investigate the classical and quantum aspects of non-commutative topological (Chern–Simons) mechanics. We introduce the magnetic field by the minimal...     

Dual wavefunctions in two–dimensional quantum mechanics

It is shown that the Schrödinger equation for a large family of pairs of two–dimensional quantum potentials possess wavefunctions for which the amplitude and the phase are interchangeable, producing two different solutions which are dual to each other. This is a property of solutions with vanishing Böhm potential. These solutions can be extended to three–dimensional systems. We explicitly calculate dual solutions for physical systems, such as the repulsive harmonic oscillator and the two–dimensional hydrogen atom. These dual wavefunctions are also solutions of an analogue optical system in the eikonal limit. In this case, the potential is related to the refractive index, allowing the study of this two–dimensional dual wavefunction solutions with an optical (analogue) system.     

Scattering states of Woods–Saxon interaction in minimal length quantum mechanics

We propose a very simple approach to deal with the problems of the modified Schrödinger equation due to minimal length and thereby solve the minimal length Schrödinger equation in the presence of a non-minimal Woods–Saxon interaction. The transmission and reflection coefficients are reported as well.     

Beyond the operator algebra—To be nonlocal realism of quantum mechanics

正In 1905,Albert Einstein presented his milestone theory of photons in his paper titled On a Heuristic Viewpoint Concerning the Production and Transformation of Lightbased on Max Planck’s black-body radiation theory.The groundbreaking theory successfully solved the paradox between Maxwell’s wave theory of light and the experimental finding     

Can the breaking of time-reversal symmetry remove degeneracies in quantum mechanics?

Reduction of spatial symmetry can remove the degeneracy of energy levels in quantum mechanics. The break of time-reversal symmetry by inclusion of a dissipative environment can have a similar effect. The corresponding time-evolution of position and momentum fluctuations can be described by a nonlinear differential equation that can lead to bifurcations and, thus, splitting of energy levels.     

A generalization of the Fényes — Nelson stochastic model of quantum mechanics

It is shown that the stochastic model of Fényes and Nelson can be generalized in such a way that the diffusion constant of the Markov theory becomes a free parameter. This extra freedom allows one to identify quantum mechanics with a class of Markov process with diffusion constants varying from 0 to .     

The role of Jahn–Teller ions in the creation of domain structures in lithium niobate

Using tightly focused laser beams, features of space charge fields (～107 V/m) are studied through the photoionization of doped Jahn–Teller Fe²⁺ ions in LiNbO₃ single crystals. These fields can be used for selective formation of the inverse domain state following the additional application of a field with a strength below the coercive field. The characteristics of laser-induced domains and periodic domain structures are studied by laser-acoustic means.     

Description of the evolution of the state of “josephson atoms” in the context of the informational interpretation of quantum mechanics

The evolution of a quantum system is informationally interpreted and used to describe decay in the coherent states of Josephson atoms, including qubits based on two- and three-junction superconducting quantum interferometers. The reduced Lindblad equation is employed to examine the measurement procedure of the Josephson qubit state and the influence of a measuring device on its coherent-state decay.