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Register a new userThermodynamics Quantities for the Klein-Gordon Equation with a Linear plus Inverse-linear Potential: Biconfluent Heun functions
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We study some thermodynamics quantities for the Klein-Gordon equation with a linear plus inverse-linear, scalar potential. We obtain the energy eigenvalues with the help of the quantization rule coming from the biconfluent Heuns equation. We use a method based on the Euler-MacLaurin formula to compute the thermal functions analytically by considering only the contribution of positive part of spectrum to the partition function.
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We study the thermodynamic quantities such as the Helmholtz free energy, the mean energy and the specific heat for both the Klein-Gordon, and Dirac equations. Our analyze includes two main subsections: ($i$) statistical functions for the Klein-Gordon equation with a linear potential having Lorentz vector, and Lorentz scalar parts ($ii$) thermodynamic functions for the Dirac equation with a Lorentz scalar, inverse-linear potential by assuming that the scalar potential field is strong ($A gg 1$). We restrict ourselves to the case where only the positive part of the spectrum gives a contribution to the sum in partition function. We give the analytical results for high temperatures.
The effective mass Klein-Gordon equation in one dimension for the Woods-Saxon potential is solved by using the Nikiforov-Uvarov method. Energy eigenvalues and the corresponding eigenfunctions are computed. Results are also given for the constant mass case.
The one-dimensional effective-mass Klein-Gordon equation for the real, and non-textrm{PT}-symmetric/non-Hermitian generalized Morse potential is solved by taking a series expansion for the wave function. The energy eigenvalues, and the corresponding eigenfunctions are obtained. They are also calculated for the constant mass case.
The dynamical symmetries of the two-dimensional Klein-Gordon equations with equal scalar and vector potentials (ESVP) are studied. The dynamical symmetries are considered in the plane and the sphere respectively. The generators of the SO(3) group corresponding to the Coulomb potential, and the SU(2) group corresponding to the harmonic oscillator potential are derived. Moreover, the generators in the sphere construct the Higgs algebra. With the help of the Casimir operators, the energy levels of the Klein-Gordon systems are yielded naturally.
The energy eigenvalues and the corresponding eigenfunctions of the one-dimensional Klein-Gordon equation with q-parameter Poschl-Teller potential are analytically obtained within the position-dependent mass formalism. The parametric generalization of the Nikiforov-Uvarov method is used in the calculations by choosing a mass distribution.
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