In this article, the linear plus modified Yukawa potential (LIMYP) is used as the quark-antiquark interaction potential for the approximate analytical bound state solution of the Klein-Gordon equation in three-dimensional space. The energy eigenvalues and associated wavefunction are obtained by solving the Klein-Gordon equation analytically using the Nikiforov-Uvarov (NU) method. The mass spectra of heavy mesons such as charmonium
(
c
c
¯
)
, bottomonium
(
b
b
¯
)
, and
b
c
¯
for various quantum states are obtained using the energy spectra expression. In comparison to experimental data, graphical modification of acquired mass spectra of heavy mesons with the parameter employed in the energy equation and the current potential provides good results.
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.
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