Energy and momentum eigenspectrum of the Hulthén-screened cosine Kratzer potential using proper quantization rule and SUSYQM method

Abstract

Using the Qiang-Dong proper quantization rule (PQR) and the supersymmetric quantum mechanics approach, we obtained the eigenspectrum of the energy and momentum for time independent and time dependent Hulth'en-screened cosine Kratzer potentials. For the suggested time independent Hulthén-screened cosine Kratzer potential, we solved the Schrödinger equation in D dimensions (HSCKP). The Feinberg-Horodecki equation for time-dependent Hulth'en-screened cosine Kratzer potential was also solved (tHSCKP). To address the inverse square term in the time independent and time dependent equations, we employed the Greene-Aldrich approximation approach. We were able to extract time independent and time dependent potentials, as well as their accompanying energy and momentum spectra. In three-dimensional space, we estimated the rotational vibrational (RV) energy spectrum for many homodimers (H 2 , I 2 , O 2 ) and heterodimers (M nH, ScN, LiH, HCl). We also used the recently introduced formula approach to obtain the relevant eigen function. We also calculated momentum spectra for the dimers M nH and ScN . The method is compared to prior methodologies for accuracy and validity using numerical data for heterodimer LiH, HCl and homodimer I 2 , O 2 , H 2 . The calculated energy and momentum spectra are tabulated and analysed.

On the Screened Kratzer Potential and Its Variants

“…Once again we conclude that all the physical results and conclusions derived from this assumption may not be correct [6]. Purohit et al [7] also proposed the Hulthén-screened cosine Kratzer potential…”

“…2r 2 e −δαr cosh(δλαr), (7) where λ is another screening parameter. Once again, the authors are unclear about the values of the screening constants.…”

“…A few years later, typical textbooks on spectroscopy [3] scarcely resort to the Kratzer potential and today no spectroscopist would take it seriously. However, several authors have recently shown some interest in the Kratzer potential and even proposed some variants [4][5][6][7][8][9][10][11][12], like the screened Kratzer potential [4,5,10], the screened cosine Kratzer potential [6], the Hulten-screened Kratzer potential [7], the improved screened Kratzer potential [8], the improved Kratzer potential [9], the shifted screened Kratzer potential [11] and the harmonic plus screened Kratzer potential [12].…”

Quarkonium spectroscopy of the linear plus modified Yukawa potential

“…Setting the discriminant in the square root equation (14) equal to zero yields the value of k. As a result, the revised eigenvalues equation is as follows:…”

“…Several researchers have used various approaches to get exact/approximate solutions of the Schrodinger, Dirac and Klein-Gordon equations using certain common potentials [1][2][3][4][5]. These methods are Nikiforov-Uvarov (NU) method [6,7], asymptotic iteration method (AIM) [8], supersymmetric quantum mechanics (SUSYQM) [9,10], factorization method [11,12], the exact quantization rule method [13] and Qiang-Dong proper quantization rule [14], etc.…”