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

Using the Qiang-Dong proper quantization rule (PQR) and the supersymmetric quantum mechanics approach, we obtain 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 (HSCKP), we solve the Schrödinger equation in D dimensions. The Feinberg-Horodecki equation for time-dependent Hulth'en-screened cosine Kratzer potential (tHSCKP) also solves. 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 estimate the rotational vibrational (RV) energy spectrum for many homodimers (H, I, O) and heterodimers (MnH, ScN, LiH, HCl). We also use the recently introduced formula approach to obtain the relevant eigen function. We also calculate momentum spectra for the dimers MnH and ScN. The method is compared to prior methodologies for accuracy and validity using numerical data for heterodimer LiH, HCl and homodimer I, O, H. The calculated energy and momentum spectra are tabulated and analyzed.