An example of dynamical systems with linear trajectory

Itô, Daisuke; Mori, K.; Carriere, Edward

doi:10.1007/bf02721775

Cited by 250 publications

(112 citation statements)

References 3 publications

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“…(3) can be absorbed into the wave function by defining 054309-3 a new spinor ψ such thatψ = e −i ψ, (16) in which = (1/hc) x V sp (x ) dx , because we have Hψ = e −i (H − αV sp )ψ. From this point on, we will refer to V t as simply a vector potential, following the common usage of this term (usually denoted by V v ).…”

Section: Equations Of Motionmentioning

confidence: 99%

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Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: The case of the relativistic harmonic oscillator

et al. 2006

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We solve the generalized relativistic harmonic oscillator in 1 + 1 dimensions, i.e., including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs. We consider positive and negative quadratic potentials and discuss in detail their bound-state solutions for fermions and antifermions. The main features of these bound states are the same as the ones of the generalized three-dimensional relativistic harmonic oscillator bound states. The solutions found for zero pseudoscalar potential are related to the spin and pseudospin symmetry of the Dirac equation in 3 + 1 dimensions. We show how the charge conjugation and γ 5 chiral transformations relate the several spectra obtained and find that for massless particles the spin and pseudospin symmetry-related problems have the same spectrum but different spinor solutions. Finally, we establish a relation of the solutions found with single-particle states of nuclei described by relativistic mean-field theories with scalar, vector, and isoscalar tensor interactions and discuss the conditions in which one may have both nucleon and antinucleon bound states.

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Section: Equations Of Motionmentioning

confidence: 99%

“…The research of this kind of interaction was started by Itô [16] and has been revived by Moshinsky and Szczepaniak [17] (see [15] for a complete reference list). In Ref.…”

Section: Introductionmentioning

confidence: 99%

Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: The case of the relativistic harmonic oscillator

et al. 2006

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“…This system was introduced in a conventional framework many years ago [24]. The interest in the problem was revived later on and the name 'Dirac oscillator' was coined to refer to it [25].…”

Section: Introductionmentioning

confidence: 99%

Lorentz-covariant deformed algebra with minimal length and application to the (1 + 1)-dimensional Dirac oscillator

Quesne¹,

Tkachuk²

2006

J. Phys. A: Math. Gen.

124

122

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The D-dimensional (β, β ′ )-two-parameter deformed algebra introduced by Kempf is generalized to a Lorentz-covariant algebra describing a (D + 1)-dimensional quantized spacetime. In the D = 3 and β = 0 case, the latter reproduces Snyder algebra. The deformed Poincaré transformations leaving the algebra invariant are identified. It is shown that there exists a nonzero minimal uncertainty in position (minimal length). The Dirac oscillator in a (1 + 1)-dimensional spacetime described by such an algebra is studied in the case where β ′ = 0. Extending supersymmetric quantum mechanical and shape-invariance methods to energy-dependent Hamiltonians provides exact bound-state energies and wavefunctions. Physically acceptable states exist for β < 1/(m 2 c 2 ). A new interesting outcome is that, in contrast with the conventional Dirac oscillator, the energy spectrum is bounded.

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“…The Dirac oscillator was introduced for the first time by Itô et al [7], in which the momentum → in Dirac equation is replaced by → − 0→ , where → is the position vector and 0 , , andã re the mass of particle, the frequency of the oscillator, and the usual Dirac matrices, respectively. Similar system was studied by Moshinsky and Szczepaniak [8], who gave it the name of Dirac oscillator; due to the nonrelativistic limit, it becomes a simple harmonic oscillator with strong spin-orbit coupling term.…”

Section: Introductionmentioning

confidence: 99%

Algebraic Approach to Exact Solution of the (2 + 1)-Dimensional Dirac Oscillator in the Noncommutative Phase Space

Panahi

Savadi

2017

Advances in High Energy Physics

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An example of dynamical systems with linear trajectory

Cited by 250 publications

References 3 publications

Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: The case of the relativistic harmonic oscillator

Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: The case of the relativistic harmonic oscillator

Lorentz-covariant deformed algebra with minimal length and application to the (1 + 1)-dimensional Dirac oscillator

Algebraic Approach to Exact Solution of the (2 + 1)-Dimensional Dirac Oscillator in the Noncommutative Phase Space

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