Abstract: In the present study, the improved screened Kratzer potential (ISKP) is investigated in the presence of external magnetic and Aharanov-Bohm (AB) fields within the framework of non-relativistic quan...

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Topics: Diatomic molecule (55%)

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20 results found

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C. O. Edet^{1}, Akpan N. Ikot^{1}, Akpan N. Ikot^{2}, Michael C. Onyeaju^{1} +4 more•Institutions (3)

Abstract: In this study, the solution of the position-dependent mass Schrodinger equation (PDMSE) for the screened Kratzer potential with the Aharanov-Bohm and position-dependent external magnetic fields are investigated using asymptotic iteration method. The energy eigenvalues and the corresponding eigenfunctions are obtained in closed form. We evaluated the partition function of the system and calculated the thermodynamic properties of the system such as Helmholtz free energy, entropy, internal energy, specific heat and the magnetization and magnetic susceptibility of the system at zero and finite temperatures.

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Topics: Partition function (statistical mechanics) (57%), Internal energy (57%), Helmholtz free energy (54%) ... show more

10 Citations

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Abstract: Confinement effects of Aharonov–Bohm (AB) flux and magnetic fields with topological defect on $$CO$$
diatomic molecule modeled by screened modified Kratzer potential is investigated in this paper. The all-encompassing effects of the fields and topological defect result in a strongly repulsive system. We discover that the collective effect of the fields and defect is more intense than the lone and dual effect and consequently there is a substantial shift in the bound state energy of the system. We also find that to sustain a low-energy medium for the molecule modeled by SMKP, the topological defect and weak AB field are required, whereas the magnetic field can be used as a control parameter or enhancer. The effects of the topological defect and magnetic and AB fields on the thermal and magnetic properties of the system are duly analyzed. We observe that the system tends to exhibit both a paramagnetic and diamagnetic behavior for weak and intense magnetic field, respectively, and some sort of saturation at high magnetic field. To further validate our findings, we map our result to 3D and a comparison of our results with what one obtains in literature reveals an excellent agreement.

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Topics: Paramagnetism (62%), Topological defect (58%), Diamagnetism (57%) ... show more

8 Citations

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Abstract: In this article, the Yukawa potential is scrutinized taking into consideration the effects of magnetic and AB flux fields within the non-relativistic regime using the factorization method. The energy equation and wave function of the system are obtained in close form. We find that the all-encompassing effects result in a strongly attractive system and consequently there is a significant upward shift in the bound state energy of the system. We also find that to achieve a low-energy medium for the Yukawa potential, weak magnetic field is required, however the AB flux field can be used as a controller. The magnetic and AB fields eliminates the degeneracy from the spectra. From our findings, it could be concluded that to manipulate the energy spectra of this system, the AB-flux and magnetic field will do so greatly. The results from this study can be applied in condensed matter physics, atomic and molecular physics.

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Topics: Yukawa potential (64%), Field (physics) (56%), Bound state (56%) ... show more

8 Citations

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Uduakobong S. Okorie^{1}, Uduakobong S. Okorie^{2}, Akpan N. Ikot^{3}, Akpan N. Ikot^{1} +4 more•Institutions (5)

Abstract: In this study, the Klein–Gordon equation (KGE) was solved with the generalized Mobius square (GMS) potential using the functional analysis approach (FAA) in D-dimensions. By employing the Pekeris-type approximation scheme, the relativistic and nonrelativistic bound state energies were obtained in closed form. Also, the expression for the scattering state phase shift of GMS potential was obtained in D-dimensions. The effects of the vibrational and rotational quantum number on the vibrational energies and the scattering state phase shift of nitrogen monoiodide (NI) diatomic molecule were studied numerically and graphically at different dimensions. An interesting result of this study is the inter-dimensional degeneracy symmetry for scattering phase shift of the NI diatomic molecule. Hence, this concept is applicable in the areas of chemical physics, nuclear and particle physics. In this study, the relativistic and nonrelativistic bound state energies of KGE with the GMS potential were obtained in D-dimensions using the FAA. In addition, the scattering state phase shift of GMS potential was obtained in D-dimensions. The effects of the vibrational and rotational quantum number on the vibrational energies and the scattering state phase shift of NI diatomic molecule were studied. The inter-dimensional degeneracy symmetry for scattering phase shift of the NI diatomic molecule was obtained at unique quantum states.

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Topics: Bound state (58%), Diatomic molecule (56%), Scattering (56%) ... show more

7 Citations

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Abstract: In this research article, quantum information-theoretic analysis of the class of Yukawa potential (CYP) has been considered in the presence of magnetic and Aharanov–Bohm (AB) fields both analytically. We solve the Schrodinger equation in the presence of external magnetic and AB fields for the CYP via the functional analysis approach to obtain the energy equation and wave function, respectively. The probability density is then obtained by squaring the wave function which is then used to obtain the Shannon entropy numerically. From our results, we note that the all-inclusive effect of the magnetic and AB fields influences the Shannon entropies such that negative values are observed, demonstrating that negative entropies exist which physically means that the probability densities are highly localized in this region. The variation in the Shannon entropy with the screening parameter $$\alpha$$
, magnetic and AB fields for the CYP is discussed. The Bialynicki-Birula, Mycielski inequality (BBM) uncertainty relation is also verified. The content of this research finds application in atomic and molecular physics, quantum chemistry and physics. In this study, Shannon information entropy is investigated with the class of Yukawa potential in position and momentum spaces in the presence of magnetic and Aharanov–Bohm (AB) fields. The all-inclusive effect of the magnetic and AB fields influences the Shannon entropies such that negative values are observed, which physically means that the probability densities are highly localized in this region. The Shannon entropy measure satisfied the Bialynicki-Birula and Mycielski (BBM) uncertainty.

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Topics: Wave function (52%), Schrödinger equation (52%), Yukawa potential (51%)

5 Citations

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45 results found

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01 Jan 1988-

Abstract: With students of Physics chiefly in mind, we have collected the material on special functions that is most important in mathematical physics and quan tum mechanics We have not attempted to provide the most extensive collec tion possible of information about special functions, but have set ourselves the task of finding an exposition which, based on a unified approach, ensures the possibility of applying the theory in other natural sciences, since it pro vides a simple and effective method for the independent solution of problems that arise in practice in physics, engineering and mathematics For the American edition we have been able to improve a number of proofs; in particular, we have given a new proof of the basic theorem ( 3) This is the fundamental theorem of the book; it has now been extended to cover difference equations of hypergeometric type ( 12, 13) Several sections have been simplified and contain new material We believe that this is the first time that the theory of classical or thogonal polynomials of a discrete variable on both uniform and nonuniform lattices has been given such a coherent presentation, together with its various applications in physics"

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Topics: Mathematical proof (56%), Special functions (55%), Fundamental theorem (55%) ... show more

1,773 Citations

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Abstract: Using solutions to a Hulth\`en-like effective potential as variational trail functions we have calculated the energy levels of the nonzero angular momentum states of the static screened Coulomb potential. Our one-parameter results for the $2p$, $3p$, $3d$, $4p$, $4d$, and $4f$ levels are in excellent agreement with earlier, more elaborate calculations. We have also calculated spontaneous emission transition probabilities between several pairs of states and find that our results compare favorably with previous calculations. We conclude that Hulth\`en-like trial functions provide better variational energies and wave functions with fewer parameters than hydrogenic or Slater-type functions for screened Coulomb and similar potentials.

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Topics: Coulomb (55%), Angular momentum (53%), Wave function (53%)

442 Citations

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Abstract: The Schrodinger equation is solved exactly for some well known potentials. Solutions are obtained reducing the Schrodinger equation into a second order differential equation by using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get energy eigenvalues and the corresponding wave functions.

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Topics: Differential equation (64%), Exact differential equation (64%), Partial differential equation (64%) ... show more

268 Citations

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Abstract: We present a closed-form expression of the classical vibrational partition function for the improved Rosen-Morse potential energy model. We give explicit expressions for the vibrational mean energy, vibrational specific heat, vibrational free energy, and vibrational entropy for diatomic molecule systems. The properties of these thermodynamic functions for the Na2 dimer are discussed in detail. We find that the improved Rosen-Morse potential model is superior to the harmonic oscillator in calculating the heat capacity for the Na2 molecules.

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Topics: Vibrational partition function (72%), Vibrational energy relaxation (66%), Ionization energy (60%) ... show more

120 Citations

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Abstract: We present a closed-form expression of the vibrational partition function for the improved Tietz potential energy model. The vibrational partition functions for the improved Manning-Rosen potential and improved Rosen-Morse potential are easily deduced as two special cases. The obtained results are applicable to many issues in chemical physics and engineering.

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Topics: Vibrational partition function (76%), Partition function (mathematics) (57%)

102 Citations