Analytical computation of amplification of coupling in relativistic equations with Yukawa potential

Energy spectrum for a modified Rosen-Morse potential solved by proper quantization rule and its thermodynamic properties

“…The latter is the generalization of the Bohr-Sommerfeld quantization rule [9] and the WKB [10][11][12]. Except for these approaches, the quasilinearization method (QLM) has played an important role in dealing with arbitrary physical potentials numerically [13][14][15][16][17][18][19][20]. Recently, Yin et al have shown why the SWKB is exact for all shape invariant potentials [21].…”

Proper quantization rule as a good candidate to semiclassical quantization rules

“…It should be noted that the exact quantization rule is a generalization of the Bohr-Sommerfeld quantization rule [15] and the Wentzel-Kramers-Brillouin (WKB) [16]. Except for these approaches mentioned above, the quasilinearization method (QLM) as another efficient and powerful approach has shown a central role in quantum mechanics [17][18][19][20][21] since QLM itself is extremely general and was applied to solve arbitrary physical potentials numerically. Recently, Yin, Cao and Shen have shown the supersymmetric Wentzel-Kramers-Brillouin (SWKB) is exact for all shape invariant potentials [22].…”

Effective-mass Klein-Gordon-Yukawa problem for bound and scattering states

“…The same numerical values of η exact is used with Ref. [22] to compare our numerical results. We plot the 1/r and the approximation 2αe −αr (1 − e −αr ) versus r. It seems that the energy eigenvalues have a good accuracy up to the values of η ≤ 0.25 and α ≤ 0.30.…”

“…We restrict ourselves for only s-states and take m 0 = 1 because of the computation in Ref. [22]. Our parameters η and α correspond to λ and k(≡ ωλ), respectively.…”