Klein Gordon Oscillator Research Articles

THREE-DIMENSIONAL KLEIN–GORDON OSCILLATOR IN A BACKGROUND MAGNETIC FIELD IN NONCOMMUTATIVE PHASE SPACE

In noncommutative phase space, wave functions and energy spectra are derived for the three-dimensional (3D) Klein–Gordon oscillator in a background magnetic field. The raising and lowering operators for this system are derived from the Heisenberg equations of motion for a 3D nonrelativistic oscillator. The coherent states are obtained as the eigenstates of the lowering operators and it is found that the coherent states are not the minimum uncertainty states due to the noncommutativity of the space. It is also pointed out that in the semiclassical limit, quantum matrix elements give solutions to the semiclassical equations.

Path integral treatment of the one-dimensional Klein–Gordon oscillator with minimal length

The path integral method is used to present an exact treatment of the one-dimensional Klein–Gordon oscillator in the context of quantum mechanics with a deformed Heisenberg algebra of the form , leading to the existence of a minimal observable length . We tackle the problem in the momentum space and we use the Schwinger proper-time method to represent Green's function. Calculations are run with the help of the point canonical transformation technique. The bound-state energy spectrum and the associated momentum space eigenfunctions are obtained, and a detailed comparison with the results for the undeformed case is made.

Comment on ‘Energy profile of the one-dimensional Klein–Gordon oscillator’

The correct energy profile of the one-dimensional Klein–Gordon oscillator, discussed by Rao and Kagali (2008 Phys. Scr. 77 015003), is obtained here by the prescription of Mirza and Mohadesi (2004 Commun. Theor. Phys.42 6646–68) and Mirza et al (2011 Commun. Theor. Phys.55 405–9). Using this prescription, the solutions are obtained in the framework of a method based on the usual annihilation and creation operators.

Klein-Gordon Oscillator in Noncommutative Phase Space Under a Uniform Magnetic Field

Using a direct substitution method, Klein-Gordon oscillator in a uniform magnetic field is researched in the noncommutative phase space (NCPS), the corresponding exact energy is obtained, and the analytic eigenfunction is presented in terms of the confluent hypergeometric. It is shown that the Klein-Gordon oscillator in uniform magnetic field in noncommutative phase space has the similar behaviors to the Landau problem in commutative space. In addition, the non-relativistic limit of the energy spectrum is obtained.

PT-symmetric operators and metastable states of the 1D relativistic oscillators

We consider the one-dimensional Dirac equation for the harmonic oscillator and the associated second-order separated operators. Such operators, defined by complex dilation, give the resonances of the problem. Their unique extensions as closed operators with a purely point spectrum are PT-symmetric with positive eigenvalues converging to the Schrödinger ones as c → ∞. Precise numerical computations show that these eigenvalues coincide with the positions of the resonances up to the order of the width. The corresponding eigenfunctions are a definite choice of metastable states of the problem. Similar results are found for the Klein–Gordon oscillator: here also we have two closed, isospectral and complex conjugate extensions of the formal operator with PT-symmetry, but an infinite number of self-adjoint extensions and physical dynamics. The infinitely many pairs of eigenvectors of the two closed PT-symmetric operators give metastable states for any choice of the dynamics. The eigenvalues of the operator defined by complex dilation are resonances, although not according to the standard definition, for any dynamics.

$\mathcal {P}\mathcal {T}$ -Symmetric Klein-Gordon Oscillator

Parity-time \((\mathcal {P}\mathcal {T})\) symmetric Klein-Gordon oscillator is presented using \(\mathcal {P}\mathcal {T}\)-symmetric minimal substitution. It is shown that wave equation is exactly solvable, and energy spectrum is the same as that of Hermitian Klein-Gordon oscillator presented by Bruce and Minning. Landau problem of \(\mathcal {P}\mathcal {T}\)-symmetric Klein-Gordon oscillator is discussed.

Exact Solution of D-Dimensional Klein–Gordon Oscillator with Minimal Length

Specific modifications of the usual canonical commutation relations between position and momentum operators have been proposed in the literature in order to implement the idea of the existence of a minimal observable length. Here, we study a consequence of this proposal in relativistic quantum mechanics by solving in the momentum space representation the Klein–Gordon oscillator in arbitrary dimensions. The exact bound states spectrum and the corresponding momentum space wave function are obtained. Following Chang et al. (Phys. Rev. D 65 (2002) 125027), we discuss constraint that can be placed on the minimal length by measuring the energy levels of an electron in a penning trap.

Wigner Functions for Klein-Gordon Oscillators in Non-commutative Space

As a quasi-probability distribution function in phase-space and as well as a special representation of the density matrix, the Wigner function is of great significance in Physics. This letter first makes a review of Wigner function and then provides three approaches of calculating it in non-commutative space. Finally, with the help of Moyal-Weyl multiplication and Bopp’s shift, the Wigner functions for Klein-Gordon oscillators in non-commutative space are deduced explicitly.

Klein-Gordon oscillators in noncommutative phase space**Supported by National Natural Science Foundation of China (10575026, 10665001, 10447005), Natural Science Foundation of Zhejiang Province, China (Y607437), and Natural Science Foundation of Education Bureau of Shaanxi Province, China (07JK207, 06JK326)

We study the Klein-Gordon oscillators in non-commutative (NC) phase space. We find that the Klein-Gordon oscillators in NC space and NC phase-space have a similar behaviour to the dynamics of a particle in commutative space moving in a uniform magnetic field. By solving the Klein-Gordon equation in NC phase space, we obtain the energy levels of the Klein-Gordon oscillators, where the additional terms related to the space-space and momentum-momentum non-commutativity are given explicitly.

DKP Oscillator in a Noncommutative Space

We present the DKP oscillator model of spins 0 and 1, in a noncommutative space. In the case of spin 0, the equation is reduced to Klein–Gordon oscillator type, the wave functions are then deduced and compared with the DKP spinless particle subjected to the interaction of a constant magnetic field. For the case of spin 1, the problem is equivalent with the behavior of the DKP equation of spin 1 in a commutative space describing the movement of a vectorial boson subjected to the action of a constant magnetic field with additional correction which depends on the noncommutativity parameter.

Energy profile of the one-dimensional Klein–Gordon oscillator

In the present paper, we describe a method of introducing the harmonic oscillator potential into the Klein–Gordon equation, leading to genuine bound states. The eigenfunctions and eigenenergies are worked out explicitly.

The Klein-Gordon and the Dirac Oscillators in a Noncommutative Space

We study the Dirac and the Klein-Gordon oscillators in a noncommutative space. It is shown that the Klein-Gordon oscillator in a noncommutative space has a similar behaviour to the dynamics of a particle in a commutative space and in a constant magnetic field. The Dirac oscillator in a noncommutative space has a similar equation to the equation of motion for a relativistic fermion in a commutative space and in a magnetic field, however a new exotic term appears, which implies that a charged fermion in a noncommutative space has an electric dipole moment.

Comment on «the Klein-Gordon oscillator» by S. Bruce and P. Minning

The different ways of description of the $S=0$ particle with oscillator-like interaction are considered. The results are in conformity with the previous paper of S. Bruce and P. Minning.