Approximate solution of Schrodinger equation in D-dimensions for scarf hyperbolic potential using Nikiforov-Uvarov method

Abstract

The approximate analytical solution of Schrodinger equation in D-Dimensions for Scarf hyperbolic potential were investigated using Nikiforov-Uvarov method. The approximate bound state energy are given in the close form and the corresponding approximate wave function for arbitary l-state in D-dimensions are formulated in the form of generalized Jacobi Polynomials. Special case is given for 5, 6, and 7 dimension from ground state to third excited state of bound state energy and wave function. The effect of the presence of this potential decreases the energy spectrum of Scarf hiperbolic potential.

Visualisasi Gelombang Sudut dalam Koordinat Bola untuk Potensial Eckart Plus Scarf dengan Pendekatan Analisis Persamaan Schrodinger Metode Nikiforov Uvarov Menggunakan Matrix Laboratory

“…Mekanika kuantum selalu menggunakan pendekatan yang berbeda untuk menentukan besaran yang terkait dengan gerak partikel yaitu menggunakan fungsi gelombang untuk merpresentasikan dinamika partikel yang bergerak yang diperoleh dari penyelesaian persamaan Schrödinger dari partikel yang berkaitan. Persamaan gerak partikel dapat diselesaikan mengunakan persamaan Schrodinger, persamaan Klein-Gordon dan persamaan Dirac [2] Beberapa metode dapat digunakan untuk menyelesaikan persamaan Schroodinger, antara lain Super Simetry (SUSY), confluence hypergeometry, Romanovsky, dan Nikiforov-Uvarov [3]. Potensial dalam kuantum menggambarkan dinamika partikel di mekanika kuantum [4].…”

“…Persamaan (46) merupakan persamaan diferensial orde dua hipergeometri, sehingga diperoleh hubungan : (cos ) = ( 2 ) 1,151 (1 + cos ) 0,651 (1 − cos ) − 0,651 (−0,02083){−24,000(1 + cos ) 3 Berdasarkan Gambar 1, dapat diketahui bahwa dengan peningkatan bilangan kuantum sudut , maka semakin banyak fungsi gelombang yang dihasilkan pada interval yang sama. Kondisi ini menunjukkan bahwa fungsi gelombang sudut engalami degenerasi.…”

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

“…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. In addition to that, hyperbolic potentials, exponential-type potentials or their combinations have attracted a lot of interest of different authors [30][31][32][33][34][35][36], both for multidimensional and lower dimensional Schrödinger equation. Bound state solutions of these potentials are very important in literature as they describe the different phenomenon like scattering, vibrational properties of molecules.…”

Bound state solutions of square root power law potential--Wavefunction ansatz method on $D$-dimensional Schrödinger equation

“…Over the past few years, theoretical physicists have shown a great deal of interest in solving higher dimensional Schrödinger equation for various potentials [1][2][3][4][5][6][7][8][9][10][11][12]. Apart from regular well known potentials, also some complicated potential like ring shaped potential coupled with Coulomb potential, exponential potential, hyperbolic potential or their different combinations are also addressed by many authors [13][14][15][16][17][18][19].…”