相关论文: Nonpointlike Particles in Harmonic Oscillators

Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…

We analyze relativistic corrections to the wave-packet dynamics of the quantum harmonic oscillator within a perturbative framework. General expressions are derived for the leading-order relativistic contributions to the wave-packet…

We establish exactly solvable models for the motion of neutral particles, electrically charged point and spin particles (U(1) symmetry), isospin particles (SU(2) symmetry), and particles with color charges (SU(3) symmetry) in a…

We study the dynamics of a quantum particle coupled to dissipative (ohmic) environments, such as an electron liquid. For some choices of couplings, the properties of the particle can be described in terms of an effective mass. A particular…

The concept of a particle is ambiguous in quantum field theory. It is generally agreed that particles depend not only on spacetime, but also on coordinates used to parametrise spacetime points. One of us has in contrast proposed a…

A class of unitary operations generated by idealized, semiclassical fields is studied. The operations implemented by sharp potential kicks are revisited and the possibility of performing them by softly varying external fields is examined.…

We construct a Hamiltonian for a quantum-mechanical model of nonrelativistic particles in three dimensions interacting via the creation and annihilation of a second type of nonrelativistic particles, which are bosons. The interaction…

In this note we consider high energy eigenfunctions of the harmonic oscillator in $\mathbb{R}^d$ and prove that any invariant measure on the energy surface can be written as a weak limit of eigenfunctions.

Classical and quantum anharmonic noncommutative oscillators with quartic self-interacting potential are considered and the effect of self-interaction term on the free energy and partition function of both models is calculated to first order…

A quantum mechanical model for the systems consisting of interacting bodies is considered. The model takes into account the noncommutativity of the space and impulse operators and the correlation equations for the indeterminacy of these…

The Einstein equations are non-linear and the particles of which the gravitational effect is described by these equations are lastly unknown. If renormalizable fields are assumed, then results are obtained only in the case of a at space.…

The definitions of classical and quantum singularities in general relativity are reviewed. The occurence of quantum mechanical singularities in certain spherically symmetric and cylindrically symmetric (including infinite line…

Quantization of the nonlinear supersymmetry faces a problem of a quantum anomaly. For some classes of superpotentials, the integrals of motion admit the corrections guaranteeing the preservation of the nonlinear supersymmetry at the quantum…

Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…

A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as…

The quantum theory of the damped harmonic oscillator has been a subject of continual investigation since the 1930s. The obstacle to quantization created by the dissipation of energy is usually dealt with by including a discrete set of…

Physical interpretations of the time-symmetric formulation of quantum mechanics, due to Aharonov, Bergmann, and Lebowitz are discussed in terms of weak values. The most direct, yet somewhat naive, interpretation uses the time-symmetric…

A rigorous quantum description of molecular dynamics with a particular emphasis on internal observables is developed accounting explicitly for kinetic couplings between nuclei and electrons. Rotational modes are treated in a genuinely…

We consider a system of two particles in noncommutative space which is rotationally invariant. It is shown that the coordinates of the center-of-mass position and the coordinates of relative motion satisfy noncommutative algebra with…

It is shown that in the rest frame of the observer in expanding Universe states of particles with negative energy exist.The properties of such states are studied. The comparison with the case of negative energies of particles in black holes…