Bound States of the Klein–gordon Equation in the Presence of Short Range Potentials

Villalba, Vı́ctor M.; Rojas, Clara

doi:10.1142/s0217751x06025158

Cited by 54 publications

(45 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…We have seen that, despite the fact that the supercritical behavior of the bound states in the one-dimensional cusp potential [13,18] is qualitatively different from the one observed for Dirac particles [5], transmission resonances possess the same structure observed for the Dirac equation. …”

mentioning

confidence: 92%

“…For an attractive cusp potential (1), given by V 0 < 0, the bound state solution of the Klein-Gordon equation can be written in terms of Whittaker functions as [18] φ L (y) = c 1 (−y)…”

mentioning

confidence: 99%

“…This state corresponds to an antiparticle emerging from the negative-energy continuum [11,18]. It is instructive to compare the scattering of a scalar Klein-Gordon particle by a cusp potential with the scattering by a square barrier.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Scattering of a relativistic scalar particle by a cusp potential

Villalba

Rojas

2007

Physics Letters A

Self Cite

View full text Add to dashboard Cite

We solve the Klein-Gordon equation in the presence of a spatially one-dimensional cusp potential. The scattering solutions are obtained in terms of Whittaker functions and the condition for the existence of transmission resonances is derived. We show the dependence of the zero-reflection condition on the shape of the potential. In the low momentum limit, transmission resonances are associated with half-bound states. We express the condition for transmission resonances in terms of the phase shifts.PACS numbers: 03.65. Pm, 03.65.Nk, 03.65.Ge The study of low-momentum scattering of nonrelativistic particles by one-dimensional potentials is a well studied and understood problem [1]. Here we have that, as momentum goes to zero, the reflection coefficient goes to unity unless the potential V (x) supports a zero energy resonance. In this case the transmission coefficient goes to unity, becoming a transmission resonance [2]. Recently, this result has been generalized to the Dirac equation [3], showing that transmission resonances at k = 0 in the Dirac equation take place for a potential barrier V = V (x) when the corresponding potential well V = −V (x) supports a supercritical state. Kennedy [4] has shown that this result is also valid for a Woods-Saxon potential. More recently, transmission resonances and half-bound states have been discussed for a Dirac particle scattered by a cusp potential [5,6] as well as for a class of short range potentials [7]. The bound states for scalar relativistic particles satisfying the Klein-Gordon equation are qualitatively different from the previous case. Here, for short-range attractive potentials the Schiff-Snyder effect [8,9,10,11,12,13,14] takes place, i.e for a given potential strength two bound states appear, one with positive norm and another with negative norm. Such states can be associated with a particle-antiparticle creation process. No antiresonant states appear [11,12].The absence of resonant overcritical states for the Klein-Gordon equation in the presence of short-range potential interactions does not prevent the existence of transmission resonances for given values of the potential.Quantum effects associated with scalar particles in the presence of external potentials have been extensively discussed in the literature [10,14]. Among quantum effects, we have that transmission resonance is one of the most interesting phenomena. For given values of the energy and the proper choice of the shape of the effective barrier, the probability of transmission reaches a maximum such as that obtained in the study of superradiance [14], where the amplitude of the scattered solutions by a rotating Kerr black hole is even larger than the amplitude of the incident wave. Analogous phenomena can also be obtained due to the presence of strong electromagnetic potentials [15].Recently, transmission resonances for the Klein-Gordon equation in the presence of a Woods-Saxon potential barrier have been computed [16]. The transmission coefficient as a function of the energy and the potential am...

show abstract

mentioning

confidence: 92%

“…For an attractive cusp potential (1), given by V 0 < 0, the bound state solution of the Klein-Gordon equation can be written in terms of Whittaker functions as [18] φ L (y) = c 1 (−y)…”

mentioning

confidence: 99%

See 1 more Smart Citation

Scattering of a relativistic scalar particle by a cusp potential

Villalba

Rojas

2007

Physics Letters A

Self Cite

View full text Add to dashboard Cite

show abstract

“…Bound state solutions of relativistic and nonrelativistic wave equation arouse a lot of interest for decades. Schrodinger wave equations constitute nonrelativistic wave equation while Klein-Gordon and Dirac equations constitute the relativistic wave equations [6][7][8][9][10]. Bound state solutions predominantly have negative energies because the energy of the particle is less than the maximum potential energy [11].…”

Section: Introductionmentioning

confidence: 99%

Approximate Solutions of Schrodinger Equation with Some Diatomic Molecular Interactions Using Nikiforov-Uvarov Method

Okon

Popoola

Isonguyo

2017

Advances in High Energy Physics

View full text Add to dashboard Cite

We used a tool of conventional Nikiforov-Uvarov method to determine bound state solutions of Schrodinger equation with quantum interaction potential called Hulthen-Yukawa inversely quadratic potential (HYIQP). We obtained the energy eigenvalues and the total normalized wave function. We employed Hellmann-Feynman Theorem (HFT) to compute expectation values ⟨ −2 ⟩, ⟨ −1 ⟩, ⟨ ⟩, and ⟨ 2 ⟩ for four different diatomic molecules: hydrogen molecule (H 2 ), lithium hydride molecule (LiH), hydrogen chloride molecule (HCl), and carbon (II) oxide molecule. The resulting energy equation reduces to three well-known potentials which are as follows: Hulthen potential, Yukawa potential, and inversely quadratic potential. The bound state energies for Hulthen and Yukawa potentials agree with the result reported in existing literature. We obtained the numerical bound state energies of the expectation values by implementing MATLAB algorithm using experimentally determined spectroscopic constant for the different diatomic molecules. We developed mathematica programming to obtain wave function and probability density plots for different orbital angular quantum number.

show abstract

“…Nevertheless, Klein and Rafelski [34] used a purported SSWE in a Coulomb potential for speculating about the Bose condensation and the stability of extremely high atomic number nuclei and, right away, were severely criticized [35]. As a matter of fact, the investigation of the bound-state solutions of the Klein-Gordon equation with different functional forms for the potential validates Popov's conjecture [28]- [29], [36]- [37].…”

Section: Introductionmentioning

confidence: 99%

Bound states of the Duffin–Kemmer–Petiau equation with a mixed minimal–nonminimal vector cusp potential

Castro¹

2010

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

Bound States of the Klein–gordon Equation in the Presence of Short Range Potentials

Abstract: We solve the Klein-Gordon equation in the presence of a spatially one-dimensional cusp potential. The bound state solutions are derived and the antiparticle bound state is discussed.

Cited by 54 publications

References 11 publications

Scattering of a relativistic scalar particle by a cusp potential

Scattering of a relativistic scalar particle by a cusp potential

Approximate Solutions of Schrodinger Equation with Some Diatomic Molecular Interactions Using Nikiforov-Uvarov Method

Bound states of the Duffin–Kemmer–Petiau equation with a mixed minimal–nonminimal vector cusp potential

Contact Info

Product

Resources

About