Solutions to the Modified Pöschl–Teller Potential inD-Dimensions

Abstract

An approximate solution of the D-dimensional Schrödinger equation with the modified Pöschl-Teller potential is obtained with an approximation of the centrifugal term. Solution to the corresponding hyper-radial equation is given using the conventional Nikiforov-Uvarov method. The normalization constants for the Pöschl-Teller potential are also computed. The expectation values r −2 , V (r) , are also obtained using the Feynman-Hellmann theorem.

A Laplace transform approach to find the exact solution of the $$N$$ N -dimensional Schrödinger equation with Mie-type potentials and construction of Ladder operators

“…Over the decades, theoretical physicists have shown a great deal of interest in solving multidimensional Schrödinger equation for various spherically symmetric potentials [1][2][3][4][5][6][7][8][9][10].These higher dimension studies provide a general treatment of the problem in such a manner that one can obtain the required results in lower dimensions just dialing appropriate N. Many analytical as well as numerical technique have been developed by researcher to investigate multidimensional Schrödinger equation for physically significant potentials [11][12][13].…”

Dirac equation with spin symmetry for the modified Pöschl–Teller potential in D dimensions

“…For example, the D-dimensional Schrödinger equation has been studied with the Coulomb-like potential [21], pseudoharmonic potential [22], Hulthén potential [23] and Pöschl-Teller potential [24]. In addition, the D-dimensional relativistic KleinGordon and Dirac equations were studied with many exactly solvable models [25][26][27][28][29][30].…”

“…The Lorentz vector V v (r ) and scalar V s (r ) modified Pöschl-Teller potential can be defined as follows [24,[39][40][41]:…”

Analytical approximate bound state solution of Schrödinger equation in D -dimensions with a new mixed class of potential for arbitrary ℓ-state via asymptotic iteration method

“…Recently, theoretical physicists have shown a great deal of interest in solving D-dimensional Schrödinger equation for various spherically symmetric potentials [11][12][13][14][15][16][17][18][19][20]. These higher dimensional studies provide a general treatment of the problem in such a manner that one can obtain the required results in lower dimensions just dialing appropriate D. Many analytical as well as numerical techniques like the Laplace transform method [21][22][23], the Nikiforov-Uvarov method [24], the algebraic method [25], the 1 N expansion method [26], the path integral approach [27], the SUSYQM [28], the exact quantization rule [29] and others are applied to address Schrödinger equation both for lower and higher dimensional cases.…”