Energy spectrum of the trigonometric Rosen–Morse potential using an improved quantization rule

Exact and approximate solutions of Schrödinger’s equation for a class of trigonometric potentials

“…It was noted that the energy eigenvalues, but not the eigenfunctions, of the Hamiltonian with the squared tangent potential on the symmetric interval (−π/2 π/2) are precisely the same as those of the Hamiltonian with the squared cotangent potential V ( ) = ν(ν −1) cot 2 on the asymmetric interval (0 π) considered by Marmorino in [12] (see also [16]). This observation can be easily verified using the identity…”

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

“…Accordingly, when applying it to calculate the energy levels we only calculate its first integral with respect to k(x), and then replace energy levels E n by E 0 to obtain the second integral. This will greatly simplify the complicated integral calculations occurred previously [6][7][8][22][23][24][25][26][27].…”

“…The exact quantization rule method is a powerful tool in finding the eigenvalues of all solvable quantum potentials [22][23][24][25][26][27]. Nevertheless, it involves complicated integral calculations, particularly the calculation of the quantum correction term.…”

Bound and Scattering State of Position Dependent Mass Klein–Gordon Equation with Hulthen Plus Deformed-Type Hyperbolic Potential

“…The exact or approximate solutions of the Klein-Gordon equation are very important in physics and chemistry because its solution contain all the necessary information needed for the complete description of the quantum state of the system such as probability density and entropy [9][10][11][12] and this quantum system is exactly solvable if all the eigenvalues and eigenfunctions can be calculated analytically [13][14][15]. In order to obtain the exact and approximate solutions of the Klein-Gordon equation, various quantum mechanical techniques have been employed such as Nikiforov-Uvarov(NU) [16], Supersymmetric quantum mechanics(SUSYQM) [17], asymptotic interation method(AIM) [18],exact quantization rule [19] and others [20]. Jia et al [21] studied the Klein-Gordon equation with improved Manning-Rosen potential using SUSYQM.…”