Analytical Bound State Solutions of the Klein-Fock-Gordon Equation for the Sum of Hulthén and Yukawa Potential within SUSY Quantum Mechanics

Abstract

The relativistic wave equations determine the dynamics of quantum fields in the context of quantum field theory. One of the conventional tools for dealing with the relativistic bound state problem is the Klein-Fock-Gordon equation. In this work, using a developed scheme, we present how to surmount the centrifugal part and solve the modified Klein-Fock-Gordon equation for the linear combination of Hulthén and Yukawa potentials. In particular, we show that the relativistic energy eigenvalues and corresponding radial wave functions are obtained from supersymmetric quantum mechanics by applying the shape invariance concept. Here, both scalar potential conditions, which are whether equal and nonequal to vector potential, are considered in the calculation. The energy levels and corresponding normalized eigenfunctions are represented as a recursion relation regarding the Jacobi polynomials for arbitrary l states. Beyond that, a closed form of the normalization constant of the wave functions is found. Furthermore, we state that the energy eigenvalues are quite sensitive with potential parameters for the quantum states. The nonrelativistic and relativistic results obtained within SUSY QM overlap entirely with the results obtained by ordinary quantum mechanics, and it displays that the mathematical implementation of SUSY quantum mechanics is quite perfect.

Point-Like Defect on Radial Solution with generalized q-deformed Hulthen Plus Class of Yukawa Potential under the Influence of Flux Field

“…Tietz potential [12], Yukawa potential [13,14], attractive radial potential [15], a general potential [16,17], anharmonic Eckart potential [18], screened Kratzer potential [19], Hulthen potential [20], hyperbolic potential [21,22], Varshni potential [23], Hellmann potential [24], inverse quadratic Yukawa potential [25], Rosen-Morse potential [26], Woods-Saxon potential [27] and many more. In addition, some combined potential models that have used to obtain solutions are Hulthen-Yukawa potential [28], Hulthen-Coulomb potential [29],…”

Generalised tanh-shaped hyperbolic potential: Klein–Gordon equation's bound state solution

“…In principle, the exponential potential models always draw considerable attention and are widely used in various physical systems, including quantum cosmology, nuclear physics, molecular physics, elementary particle physics, and condensed matter physics [19][20][21][22][23][24][25][26][27][28][29]. Up to now, many exponential-type potentials, including the Morse [30,31], Hulthén [32][33][34][35][36][37][38], Woods-Saxon [27,[39][40][41][42][43], Rosen-Morse [44][45][46][47][48], Eckart-type [49][50][51], Manning-Rosen [52][53][54], Deng-Fan [55,56], Pöschl-Teller like [57], Mathieu [58], sine-type hyperbolic [59] and Schiöberg [60][61][62][63] potentials have been investigated, and some analytical bound state solutions were obtained using an approximation for these models ...…”

Approximate analytical solutions of the Schrodinger equation in central potential field

“…A combination of two potentials has aroused extensive research interest in literature. Many researchers have adopted this type of potential to carry out some works [8,9,10,11,12,13,14,15]. Motivated by these works, we consider the following form of potential model which is the superposition of Hulthn [16] and a class of Yukawa [17] potentials…”