Analytical Solutions to the Klein–Gordon Equation with Position-Dependent Mass for q -Parameter Pöschl–Teller Potential

Abstract

The energy eigenvalues and the corresponding eigenfunctions of the one-dimensional KleinGordon equation with q-parameter Pöschl-Teller potential are analytically obtained within the position-dependent mass formalism. The parametric generalization of the Nikiforov-Uvarov method is used in the calculations by choosing a mass distribution.

Analytical solutions of position-dependent mass Klein–Gordon equation for unequal scalar and vector Yukawa potentials

“…On the other hand, the problem of the position-dependent mass in the quantum mechanical systems, has also caused increasing interests and inspired some research activities [8][9][10][11]. This formalism has been widely used in different areas of physics such as materials science and condensed matter physics like compositionally graded crystals [12], in depicting quantum dots and the transport properties of semiconductors [13], in metal clusters [14], 3He clusters [15], the energy density many-body problem [16] and quantum liquids [17].…”

Interaction of Spinless Particles with Yukawa Ring-Shaped Potential

“…When we set = = = 0 in Eq. (32), the Yukawa ring-shaped potential reduces to Yukawa potential and the energy eigenvalues are obtained as follows [21]: pure angle dependent potential could be obtained by using this adjusted parameters of Eq. (68).…”

“…These equations are solved by means of different methods for exactly solvable potentials such as Supersymmetry Quantum Mechanics (SUSYQM) [6][7][8][9][10][11], time-dependent perturbation [12], asymptotic iteration method (AIM) [13][14][15][16], factorization method [17,18], functional analysis [19], Nikiforov-Uvarov (NU) method [20][21][22][23][24][25][26][27][28], and others [29][30][31]. Yaşuk et al [8] presented an alternative simple method for the exact solution of the Klein-Gordon equation (KGE) in the presence of noncentral equal scalar and vector potentials, by using the Nikiforov-Uvarov method [45].…”

Bound states of the Duffin--Kemmer--Petiau equation for square potential well with position-dependent mass

“…In the relativistic case, in order to explain some associated quantum effects, the Klein-Gordon (KG) particle with spin 0 and the Dirac particle with spin 1/2 within an effective mass and in different forms of potential have also been examined [17][18][19][20][21][22][23][24][25][26]. For example, the spectrum of the D-dimensional Dirac equation, where the mass is dependent on the position and within the framework of an exponential for the centrifugal term, was obtained in [27], and the N-dimensional Pöschl-Teller potential with PDM was also considered in [28], using the asymptotic iteration method.…”