The WKB Method for the Dirac Equation with the Vector and Scalar Potentials

Rubish, V. V.; Lazur, V. Yu.; Reity, O. K.; Chalupka, S.; Salak, M.

doi:10.1023/b:cjop.0000042643.47049.98

Cited by 11 publications

(33 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…which is valid for both signs of k [16]. The obtained quasiclassical formula (10) is the relativistic generalization of the well-known Gamow formula for the width of a quasistationary level.…”

Section: Quasiclassical Approximation For the Dirac Equation Withmentioning

confidence: 62%

“…where Q = q + |k|r −1 . The solution for the states with k < 0 can be found in [16]. iii) in the "exterior" classically allowed region r > r 2 , a quasistationary state is associated with the divergent wave…”

Section: Quasiclassical Approximation For the Dirac Equation Withmentioning

confidence: 99%

“….. In [16] the system (1) was consecutively solved using the known technique of left and right eigenvectors of the homogeneous system. For the effective potential (EP) of the barrier type (see Fig.…”

Section: Quasiclassical Approximation For the Dirac Equation Withmentioning

confidence: 99%

“…where the period T of radial oscillations of the classical relativistic particle is given by the formula T = 2 r1 r0 (E − V (r))/p(r) dr [16].…”

Section: The Mass Spectrum Of Heavy-light Quark Systemsmentioning

confidence: 99%

“…The construction of quasiclassical solutions of the spinor equation with a scalar-vector interaction was reported in [15,16]. The scheme of quasiclassical quantization proposed in [16] allows to make clear the connection of quasiclassical asymptotic behavior in spectral prob-lems for the Dirac equation in external scalar and vector fields with the Lorentz structure of interaction potentials corresponding to them.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Quasiclassical theory of the Dirac equation with a scalar-vector interaction and its applications in the physics of heavy-light mesons

2011

View full text Add to dashboard Cite

We construct a relativistic potential quark model of D, Ds, B, and Bs mesons in which the light quark motion is described by the Dirac equation with a scalar-vector interaction and the heavy quark is considered a local source of the gluon field. The effective interquark interaction is described by a combination of the perturbative one-gluon exchange potential V Coul (r) = −ξ/r and the long-range Lorentz-scalar and Lorentz-vector linear potentials S l.r. (r) = (1 − λ)(σr + V0) and V l.r. (r) = λ(σr + V0), where 0 λ < 1/2. Within the quasiclassical approximation, we obtain simple asymptotic formulas for the energy and mass spectra and for the mean radii of D, Ds, B, and Bs mesons, which ensure a high accuracy of calculations even for states with the radial quantum number nr ∼ 1. We show that the fine structure of P-wave states in heavy-light mesons is primarily sensitive to the choice of two parameters: the strong-coupling constant αs and the coefficient λ of mixing of the long-range scalar and vector potentials S l.r. (r) and V l.r. (r). The quasiclassical formulas for asymptotic coefficients of wave function at zero and infinity are obtained.

show abstract

Section: Quasiclassical Approximation For the Dirac Equation Withmentioning

confidence: 62%

Section: Quasiclassical Approximation For the Dirac Equation Withmentioning

confidence: 99%

Section: Quasiclassical Approximation For the Dirac Equation Withmentioning

confidence: 99%

“…where the period T of radial oscillations of the classical relativistic particle is given by the formula T = 2 r1 r0 (E − V (r))/p(r) dr [16].…”

Section: The Mass Spectrum Of Heavy-light Quark Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Quasiclassical theory of the Dirac equation with a scalar-vector interaction and its applications in the physics of heavy-light mesons

2011

View full text Add to dashboard Cite

show abstract

Semiclassical approximation in the relativistic potential model of B and D mesons

2008

View full text Add to dashboard Cite

We construct a relativistic potential quark model of D, Ds, B, and Bs mesons in which the light quark motion is described by the Dirac equation with a scalar-vector interaction and the heavy quark is considered a local source of the gluon field. The effective interquark interaction is described by a combination of the perturbative one-gluon exchange potential V Coul (r) and the long-range Lorentz-scalar and Lorentz-vector linear potentials S l.r. (r) and V l.r. (r). In the semiclassical approximation, we obtain simple asymptotic formulas for the energy and mass spectra and for the mean radii of D, Ds, B, and Bs mesons, which ensure a high accuracy of calculations even for states with the radial quantum number nr ∼ 1. We show that the fine structure of P-wave states in heavy-light mesons is primarily sensitive to the choice of two parameters: the strong-coupling constant αs and the coefficient λ of mixing of the long-range scalar and vector potentials S l.r. (r) and V l.r. (r).

show abstract

Evolution of quasi-bound states in the circular n–p junction of bilayer graphene under magnetic field

Pan

Liu

2020

Sci Rep

View full text Add to dashboard Cite

Electron in gapless bilayer graphene can form quasi-bound states when a circular symmetric potential is created in bilayer graphene. These quasi-bound states can be adjusted by tuning the radius and strength of the potential barrier. We investigate the evolution of quasi-bound states spectra in the circular n–p junction of bilayer graphene under the magnetic field numerically. The energy levels of opposite angular momentum split and the splitting increases with the magnetic field. Moreover, weak magnetic fields can slightly shift the energy levels of quasi-bound states. While strong magnetic fields induce additional resonances in the local density states, which originates from Landau levels. We demonstrate that these numerical results are consistent with the semiclassical analysis based on Wentzel–Kramers–Brillouin approximation. Our results can be verified experimentally via scanning tunneling microscopy measurements.

show abstract

The WKB Method for the Dirac Equation with the Vector and Scalar Potentials

Cited by 11 publications

References 16 publications

Quasiclassical theory of the Dirac equation with a scalar-vector interaction and its applications in the physics of heavy-light mesons

Quasiclassical theory of the Dirac equation with a scalar-vector interaction and its applications in the physics of heavy-light mesons

Semiclassical approximation in the relativistic potential model of B and D mesons

Evolution of quasi-bound states in the circular n–p junction of bilayer graphene under magnetic field

Contact Info

Product

Resources

About