Approximate Analytical Solutions to the Generalized Pöschl—Teller Potential in D Dimensions

Abstract

The Schrödinger equation for the generalized Pöschl-Teller potential with the centrifugal term is investigated approximately. The Nikiforov-Uvarov method is used in the calculations and the eigenfunctions as well as the energy eigenvalues obtained after a proper Pekeris-type approximation. Some useful expectation values and the oscillator strength are reported.

Solutions of Schrodinger equation for the modified Mobius square plus Kratzer potential

“…In theoretical physics and other physics-related fields, much research interest has been directed toward obtaining and discussing the exact solutions of Schrodinger wave equation for different potentials, during the past years [1][2][3][4][5]. The reason is because the solutions contain sufficient information to explain the quantum system under probe.…”

Analisis Spektrum Energi dan Fungsi Gelombang Potensial Non-Sentral Poschl-Teller Termodifikasi plus Potensial Scarf Trigonometri Menggunakan Persamaan Hipergeometri (Halaman 41 s.d. 47)

“…Persamaan Schrodinger (PS) untuk potensial yang merupakan fungsi hiperbolik, eksponensial dan trigonometrik seperti Poschl-Teller [1,3,4,5,6,7], Scarf [1,3,8], Morse [1,3], Rosen-Morse [1,3,5,11], Wood-Saxon [1,3,9], Eckart [1,3,10], Hulthen [1,3] dapat diselesaikan dengan menggunakan SUSY MK [1,3,11], Nikivarov Ufarov (NU) [12,13] dan persamaan hipergeometri [1]. Namun aplikasi persamaan hipergeometri lebih luas dari pada SUSY MK karena dapat digunakan untuk menyelesaiakan PS potensial baik shape invariance (SI) dan non-shape invariance (NSI) sedangkan SUSY MK hanya untuk potensial shape invariance saja.…”

“…n a a a a a a n (7) dan 1 ) ( 0 = a Penyelesaian persamaan diferensial fungsi hipergeometri yang dinyatakan pada persamaan (6) di atas mempunyai harga bila semua penyebut dari deret tersebut tidak nol, maka c≠ -n, dimana n = 0, 1, 2, 3, 4, ...... Bila a = -n atau b = -n,…”

Approximate eigensolutions of the attractive potential via parametric Nikiforov-Uvarov method

“…Thus, the exact solutions of the wave equation with the various potential models have attracted much attention from many authors since they contain all the necessary information to study the quantum models. It is well known that there are various traditional techniques used to solve the relativistic and non-relativistic wave equations with the various quantum potential models [1, 2, 3, 4, 5, 6, 7, 8]. These techniques include asymptotic iteration method [9, 10, 11], supersymmetric approach [12, 13, 14, 15], factorization method [16, 17], Nikiforov-Uvarov method [18, 19, 20], exact/proper quantization rule [21], 1/N shifted expansion method [22].…”