Application of formula method for bound state problems in Schrödinger equation

Abstract The study presents the thermodynamic properties of the Iodine and Scandium Flouride molecules with molecular Deng-Fan potential. The bound state energy solution of the radial Schrodinger equation is obtained via the formula method. The partition function and other thermodynamic properties are evaluated via the Poisson summation approach. The numerical values of energy of the I2 and ScF molecules are found to be in agreement with results obtained from other methods in the literature. The results further show that the partition function decreases, and then converges to a constant value as temperature increases.

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Solutions of Schrodinger Equation And Thermodynamic Properties of Potassium Dimer Based On Formular Method

10.21203/rs.3.rs-763444/v1 ◽

2021 ◽

Author(s):

C. P. Onyenegecha ◽

E. N. Omoko ◽

I. J. Njoku ◽

E. E. Oguzie ◽

C. J. Okereke

Keyword(s):

Partition Function ◽

Thermodynamic Properties ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

State Energy ◽

Bound State ◽

Bound State Energy ◽

Radial Schrödinger Equation ◽

Potassium Dimer ◽

Formula Method

Abstract The study presents the thermodynamic properties of the XI Σ+g state of potassium (K2) dimer with molecular Deng-Fan potential. The bound state energy solution of the radial Schrodinger equation is obtained via the formula method. The partition function and other thermodynamic properties are evaluated. The numerical values of energy are found to be in agreement with results obtained from other methods in literature. The results further show that the partition function increases as temperature decreases, which implies a decrease in the probability of finding a particle in a state with quantum number, n.

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The Nonlinear Schrödinger Equation for Orthonormal Functions II: Application to Lieb–Thirring Inequalities

Communications in Mathematical Physics ◽

10.1007/s00220-021-04039-5 ◽

2021 ◽

Author(s):

Rupert L. Frank ◽

David Gontier ◽

Mathieu Lewin

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Bound State ◽

Nonlinear Schrodinger Equation ◽

Best Constant ◽

Nonlinear Schrödinger ◽

The One ◽

Bound State Case ◽

Cubic Nonlinear Schrödinger Equation

AbstractIn this paper we disprove part of a conjecture of Lieb and Thirring concerning the best constant in their eponymous inequality. We prove that the best Lieb–Thirring constant when the eigenvalues of a Schrödinger operator $$-\Delta +V(x)$$ - Δ + V ( x ) are raised to the power $$\kappa $$ κ is never given by the one-bound state case when $$\kappa >\max (0,2-d/2)$$ κ > max ( 0 , 2 - d / 2 ) in space dimension $$d\ge 1$$ d ≥ 1 . When in addition $$\kappa \ge 1$$ κ ≥ 1 we prove that this best constant is never attained for a potential having finitely many eigenvalues. The method to obtain the first result is to carefully compute the exponentially small interaction between two Gagliardo–Nirenberg optimisers placed far away. For the second result, we study the dual version of the Lieb–Thirring inequality, in the same spirit as in Part I of this work Gontier et al. (The nonlinear Schrödinger equation for orthonormal functions I. Existence of ground states. Arch. Rat. Mech. Anal, 2021. https://doi.org/10.1007/s00205-021-01634-7). In a different but related direction, we also show that the cubic nonlinear Schrödinger equation admits no orthonormal ground state in 1D, for more than one function.

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EXACT SOLUTION OF THE SCHRÖDINGER EQUATION FOR THE MODIFIED KRATZER'S MOLECULAR POTENTIAL WITH POSITION-DEPENDENT MASS

International Journal of Modern Physics E ◽

10.1142/s0218301308010428 ◽

2008 ◽

Vol 17 (07) ◽

pp. 1327-1334 ◽

Cited By ~ 22

Author(s):

RAMAZÀN SEVER ◽

CEVDET TEZCAN

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

State Energy ◽

Bound State ◽

Bound State Energy ◽

Energy Eigenvalues ◽

Molecular Potential ◽

Dependent Mass ◽

Morse Potentials ◽

Position Dependent Mass

Exact solutions of Schrödinger equation are obtained for the modified Kratzer and the corrected Morse potentials with the position-dependent effective mass. The bound state energy eigenvalues and the corresponding eigenfunctions are calculated for any angular momentum for target potentials. Various forms of point canonical transformations are applied.

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Bound state solutions of Schrödinger equation with modified Mobius square potential (MMSP) and its thermodynamic properties

Journal of Molecular Modeling ◽

10.1007/s00894-018-3811-8 ◽

2018 ◽

Vol 24 (10) ◽

Cited By ~ 22

Author(s):

Uduakobong S. Okorie ◽

Akpan N. Ikot ◽

Michael C. Onyeaju ◽

Ephraim O. Chukwuocha

Keyword(s):

Thermodynamic Properties ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Bound State ◽

Modified Mobius Square Potential

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Bound State Solutions of the Schrödinger Equation

Quantum Mechanics: Theory and Applications ◽

10.1007/978-1-4020-2130-5_6 ◽

2004 ◽

pp. 115-158

Author(s):

Ajoy Ghatak ◽

S. Lokanathan

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Bound State

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Analytical solutions of fractional Schrödinger equation and thermal properties of Morse potential for some diatomic molecules

Modern Physics Letters A ◽

10.1142/s0217732321500413 ◽

2021 ◽

pp. 2150041

Author(s):

U. S. Okorie ◽

A. N. Ikot ◽

G. J. Rampho ◽

P. O. Amadi ◽

Hewa Y. Abdullah

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Morse Potential ◽

State Energy ◽

Diatomic Molecules ◽

Bound State ◽

Bound State Energy ◽

Fractional Schrödinger Equation ◽

Energy Eigenvalues ◽

Fractional Schrodinger Equation

By employing the concept of conformable fractional Nikiforov–Uvarov (NU) method, we solved the fractional Schrödinger equation with the Morse potential in one dimension. The analytical expressions of the bound state energy eigenvalues and eigenfunctions for the Morse potential were obtained. Numerical results for the energies of Morse potential for the selected diatomic molecules were computed for different fractional parameters chosen arbitrarily. Also, the graphical variation of the bound state energy eigenvalues of the Morse potential for hydrogen dimer with vibrational quantum number and the range of the potential were discussed, with regards to the selected fractional parameters. The vibrational partition function and other thermodynamic properties such as vibrational internal energy, vibrational free energy, vibrational entropy and vibrational specific heat capacity were evaluated in terms of temperature. Our results are new and have not been reported in any literature before.

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Bound state solution of the Schrodinger equation for the Woods–Saxon potential plus coulomb interaction by Nikiforov–Uvarov and supersymmetric quantum mechanics methods

International Journal of Modern Physics E ◽

10.1142/s0218301321500233 ◽

2021 ◽

pp. 2150023

Author(s):

Enayatolah Yazdankish

Keyword(s):

Quantum Mechanics ◽

Schrödinger Equation ◽

Coulomb Interaction ◽

Schrodinger Equation ◽

Energy Eigenvalue ◽

Bound State ◽

Repulsive Interaction ◽

Saxon Potential ◽

Special Cases ◽

Supersymmetry Quantum Mechanics

The generalized Woods–Saxon potential plus repulsive Coulomb interaction is considered in this work. The supersymmetry quantum mechanics method is used to get the energy spectrum of Schrodinger equation and also the Nikiforov–Uvarov approach is employed to solve analytically the Schrodinger equation in the framework of quantum mechanics. The potentials with centrifugal term include both exponential and radial terms, hence, the Pekeris approximation is considered to approximate the radial terms. By using the step-by-step Nikiforov–Uvarov method, the energy eigenvalue and wave function are obtained analytically. After that, the spectrum of energy is obtained by the supersymmetry quantum mechanics method. The energy eigenvalues obtained from each method are the same. Then in special cases, the results are compared with former result and a full agreement is observed. In the [Formula: see text]-state, the standard Woods–Saxon potential has no bound state, but with Coulomb repulsive interaction, it may have bound state for zero angular momentum.

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