scholarly journals QUANTUM MECHANICS IN NONINERTIAL FRAMES WITH A MULTITEMPORAL QUANTIZATION SCHEME II: NONRELATIVISTIC PARTICLES

2006 ◽  
Vol 21 (19n20) ◽  
pp. 3917-3945 ◽  
Author(s):  
DAVID ALBA
Keyword(s):  
Quantum Mechanics ◽  
Bound States ◽  
Center Of Mass ◽  
Quantization Scheme ◽  
Unitary Evolution ◽  
Classical Level ◽  
Noninertial Effects ◽  
Special Cases ◽  
Relativistic Particles

The nonrelativistic version of the multitemporal quantization scheme of relativistic particles in a family of noninertial frames (see Ref. 1) is defined. At the classical level the description of a family of nonrigid noninertial frames, containing the standard rigidly linear accelerated and rotating ones, is given in the framework of parametrized Galilei theories. Then the multitemporal quantization, in which the gauge variables, describing the noninertial effects, are not quantized but considered as c-number generalized times, is applied to nonrelativistic particles. It is shown that with a suitable ordering there is unitary evolution in all times and that, after the separation of the center-of-mass, it is still possible to identify the inertial bound states. The few existing results of quantization in rigid noninertial frames are recovered as special cases.

scholarly journals QUANTUM MECHANICS IN NONINERTIAL FRAMES WITH A MULTITEMPORAL QUANTIZATION SCHEME I: RELATIVISTIC PARTICLES

2006 ◽  
Vol 21 (13n14) ◽  
pp. 2781-2851 ◽  
Author(s):  
DAVID ALBA ◽  
LUCA LUSANNA
Keyword(s):  
Quantum Mechanics ◽  
Center Of Mass ◽  
Energy Operator ◽  
Relative Energy ◽  
Time Dependent ◽  
Positive Energy ◽  
Quantization Scheme ◽  
Effective Hamiltonian ◽  
Unitary Evolution ◽  
Inertial Energy

After a review of the few attempts to define quantum mechanics in noninertial frames, we introduce a family of relativistic nonrigid noninertial frames (equal-time parallel hyper-planes with differentially rotating 3-coordinates) as a gauge fixing of the description of N positive energy particles in the framework of parametrized Minkowski theories. Then we define a multitemporal quantization scheme in which the particles are quantized, but not the gauge variables describing the noninertial frames: they are considered as c-number generalized times. We study the coupled Schrödinger-like equations produced by the first class constraints and we show that there is a physical scalar product independent both from time and generalized times and a unitary evolution. Since a path in the space of the generalized times defines a nonrigid noninertial frame, we can find the associated self-adjoint effective Hamiltonian [Formula: see text] for the noninertial evolution: it differs from the inertial energy operator for the presence of inertial potentials and turns out to be frame-dependent like the energy density in general relativity. After a separation of the relativistic center of mass from the relative variables by means of a recently developed relativistic kinematics, inside [Formula: see text] we can identify the self-adjoint relative energy operator (the invariant mass) [Formula: see text] corresponding to the inertial energy and producing the same levels for the spectra of atoms as in inertial frames. Instead the (in general time-dependent) effective Hamiltonian is responsible for the interferometric effects signaling the noninertiality of the frame. It cannot be interpreted as an energy (there is no relativity principle and no kinematic group in noninertial frames) and generically, like in the case of time-dependent c-number external electromagnetic fields, it has no associated eigenvalue equation defining a noninertial spectrum. This formulation should help to find relativistic Bel inequalities and to define a quantization scheme for canonical gravity after having found a ultraviolet regularization of the Tomonaga–Schwinger formalism in special relativity as required by the Torre–Varadarajan no-go theorem.

scholarly journals Noninertial effects on a scalar field in a spacetime with a magnetic screw dislocation

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Ricardo L. L. Vitória
Keyword(s):  
Scalar Field ◽  
Screw Dislocation ◽  
Bound States ◽  
Charged Scalar ◽  
Wall Potential ◽  
Noninertial Effects ◽  
Klein Gordon ◽  
Coulomb Type ◽  
Charged Scalar Field ◽  
Type Potential

Abstract We investigate rotating effects on a charged scalar field immersed in spacetime with a magnetic screw dislocation. In addition to the hard-wall potential, which we impose to satisfy a boundary condition from the rotating effect, we insert a Coulomb-type potential and the Klein–Gordon oscillator into this system, where, analytically, we obtain solutions of bound states which are influenced not only by the spacetime topology, but also by the rotating effects, as a Sagnac-type effect modified by the presence of the magnetic screw dislocation.

scholarly journals Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states

2019 ◽  
Vol 2019 (10) ◽  
Author(s):  
Fernando Romero-López ◽  
Stephen R. Sharpe ◽  
Tyler D. Blanton ◽  
Raúl A. Briceño ◽  
Maxwell T. Hansen
Keyword(s):  
Finite Volume ◽  
Bound States ◽  
Numerical Exploration ◽  
Relativistic Particles

scholarly journals On relativistic entanglement and localization of particles and on their comparison with the nonrelativistic theory

2014 ◽  
Vol 29 (29) ◽  
pp. 1450163 ◽  
Author(s):  
Horace W. Crater ◽  
Luca Lusanna
Keyword(s):  
Bound States ◽  
Clock Synchronization ◽  
Center Of Mass ◽  
Particle Beams ◽  
Open Problems ◽  
Inertial Frames ◽  
Classical Trajectories ◽  
Particle Localization ◽  
Relativistic Bound States ◽  
Classical And Quantum Mechanics

We make a critical comparison of relativistic and nonrelativistic classical and quantum mechanics of particles in inertial frames as well of the open problems in particle localization at both levels. The solution of the problems of the relativistic center-of-mass, of the clock synchronization convention needed to define relativistic 3-spaces and of the elimination of the relative times in the relativistic bound states leads to a description with a decoupled nonlocal (nonmeasurable) relativistic center-of-mass and with only relative variables for the particles (single particle subsystems do not exist). We analyze the implications for entanglement of this relativistic spatial nonseparability not existing in nonrelativistic entanglement. Then, we try to reconcile the two visions showing that also at the nonrelativistic level in real experiments only relative variables are measured with their directions determined by the effective mean classical trajectories of particle beams present in the experiment. The existing results about the nonrelativistic and relativistic localization of particles and atoms support the view that detectors only identify effective particles following this type of trajectories: these objects are the phenomenological emergent aspect of the notion of particle defined by means of the Fock spaces of quantum field theory.

Mathematical aspects of trapping modes in the theory of surface waves

1987 ◽  
Vol 183 ◽  
pp. 421-437 ◽  
Author(s):  
F. Ursell
Keyword(s):  
Bound States ◽  
Constant Width ◽  
Minimum Energy ◽  
Horizontal Cylinder ◽  
Linear Operators ◽  
Inviscid Fluid ◽  
Infinite Length ◽  
Horizontal Canal ◽  
Special Cases ◽  
Characteristic Modes

A horizontal canal of infinite length and of constant width and depth contains inviscid fluid under gravity. The fluid is bounded internally by a submerged horizontal cylinder which extends right across the canal and has its generators normal to the sidewalls. Suppose that the fluid is set in motion by a surface pressure varying across the canal, then some of the energy is radiated to infinity while some of the energy is trapped in characteristic modes (bound states) near the cylinder. The existence of trapping modes in special cases was shown by Stokes (1846) and Ursell (1951); a general treatment, given by Jones (1953), is based on the theory of elliptic partial differential equations in unbounded domains. In the present paper a much simpler treatment is given which uses only the theory of bounded symmetric linear operators together with Kelvin's minimum-energy theorem of classical hydrodynamics.

scholarly journals WKB FORMALISM AND A LOWER LIMIT FOR THE ENERGY EIGENSTATES OF BOUND STATES FOR SOME POTENTIALS

2007 ◽  
Vol 22 (35) ◽  
pp. 2675-2687 ◽  
Author(s):  
LUIS F. BARRAGÁN-GIL ◽  
ABEL CAMACHO
Keyword(s):  
Quantum Mechanics ◽  
Gravitational Field ◽  
Lower Bound ◽  
Harmonic Oscillator ◽  
Approximation Method ◽  
Bound States ◽  
The Other ◽  
Homogeneous Gravitational Field ◽  
Definition Of ◽  
Ground Energy

In this work the conditions appearing in the so-called WKB approximation formalism of quantum mechanics are analyzed. It is shown that, in general, a careful definition of an approximation method requires the introduction of two length parameters, one of them always considered in the textbooks on quantum mechanics, whereas the other is usually neglected. Afterwards we define a particular family of potentials and prove, resorting to the aforementioned length parameters, that we may find an energy which is a lower bound to the ground energy of the system. The idea is applied to the case of a harmonic oscillator and also to a particle freely falling in a homogeneous gravitational field, and in both cases the consistency of our method is corroborated. This approach, together with the so-called Rayleigh–Ritz formalism, allows us to define an energy interval in which the ground energy of any potential, belonging to our family, must lie.

Bound state solution of the Schrodinger equation for the Woods–Saxon potential plus coulomb interaction by Nikiforov–Uvarov and supersymmetric quantum mechanics methods

2021 ◽  
pp. 2150023
Author(s):  
Enayatolah Yazdankish
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Interaction ◽  
Schrodinger Equation ◽  
Energy Eigenvalue ◽  
Bound State ◽  
Repulsive Interaction ◽  
Saxon Potential ◽  
Special Cases ◽  
Supersymmetry Quantum Mechanics

The generalized Woods–Saxon potential plus repulsive Coulomb interaction is considered in this work. The supersymmetry quantum mechanics method is used to get the energy spectrum of Schrodinger equation and also the Nikiforov–Uvarov approach is employed to solve analytically the Schrodinger equation in the framework of quantum mechanics. The potentials with centrifugal term include both exponential and radial terms, hence, the Pekeris approximation is considered to approximate the radial terms. By using the step-by-step Nikiforov–Uvarov method, the energy eigenvalue and wave function are obtained analytically. After that, the spectrum of energy is obtained by the supersymmetry quantum mechanics method. The energy eigenvalues obtained from each method are the same. Then in special cases, the results are compared with former result and a full agreement is observed. In the [Formula: see text]-state, the standard Woods–Saxon potential has no bound state, but with Coulomb repulsive interaction, it may have bound state for zero angular momentum.

Sign in / Sign up

Export Citation Format

Share Document