scholarly journals On solutions of the Schrödinger equation for some molecular potentials: wave function ansatz

Open Physics ◽  
2008 ◽  
Vol 6 (3) ◽  
Author(s):  
Sameer Ikhdair ◽  
Ramazan Sever
Keyword(s):  
Wave Function ◽  
Angular Momentum ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound State ◽  
Angular Momentum Quantum Number ◽  
Radial Schrödinger Equation ◽  
Spatial Dimensions ◽  
Molecular Potentials ◽  
The Given

AbstractMaking an ansatz to the wave function, the exact solutions of the D-dimensional radial Schrödinger equation with some molecular potentials, such as pseudoharmonic and modified Kratzer, are obtained. Restrictions on the parameters of the given potential, δ and ν are also given, where η depends on a linear combination of the angular momentum quantum number ℓ and the spatial dimensions D and δ is a parameter in the ansatz to the wave function. On inserting D = 3, we find that the bound state eigensolutions recover their standard analytical forms in literature.

Exact solution of D-dimensional Schrödinger equation generated from certain central power-law potentials

Open Physics ◽  
2014 ◽  
Vol 12 (4) ◽  
Author(s):  
Nabaratna Bhagawati
Keyword(s):  
Exact Solution ◽  
Schrödinger Equation ◽  
Power Law ◽  
Schrodinger Equation ◽  
Transformation Method ◽  
Angular Momentum Quantum Number ◽  
Exactly Solvable Potentials ◽  
Radial Schrödinger Equation ◽  
Exactly Solvable ◽  
The Given

AbstractBy applying Extended Transformation method we have generated exact solution of D-dimensional radial Schrödinger equation for a set of power-law multi-term potentials taking singular potentials $$V(r) = ar^{ - \tfrac{1} {2}} + br^{ - \tfrac{3} {2}}$$, $$V(r) = ar^{\tfrac{2} {3}} + br^{ - \tfrac{2} {3}} + cr^{ - \tfrac{4} {3}}$$, V(r) = ar + br −1 + cr 2 and V(r) = ar 2+br −2+cr −4+dr −6 as input reference. The restriction on the parameters of the given potentials and angular momentum quantum number ℓ are obtained. The multiplet structure of the generated exactly solvable potentials are also shown.

Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

2018 ◽  
Vol 2 (2) ◽  
pp. 43-47
Author(s):  
A. Suparmi, C. Cari, Ina Nurhidayati
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Energy Spectra ◽  
Atomic Particle ◽  
Approximate Analytical Solutions ◽  
Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The  Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

scholarly journals The bound state solutions of the D-dimensional Schrödinger equation for the Woods–Saxon potential

2016 ◽  
Vol 25 (01) ◽  
pp. 1650002 ◽  
Author(s):  
V. H. Badalov
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound State ◽  
Wave Functions ◽  
Saxon Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Quantum Numbers ◽  
Radial Schrödinger Equation ◽  
Pekeris Approximation

In this work, the analytical solutions of the [Formula: see text]-dimensional radial Schrödinger equation are studied in great detail for the Wood–Saxon potential by taking advantage of the Pekeris approximation. Within a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any angular momentum case within the context of the Nikiforov–Uvarov (NU) and Supersymmetric quantum mechanics (SUSYQM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformed each other is demonstrated. In addition, a finite number energy spectrum depending on the depth of the potential [Formula: see text], the radial [Formula: see text] and orbital [Formula: see text] quantum numbers and parameters [Formula: see text] are defined as well.

Analysis of Regge poles for the Schrödinger equation

2009 ◽  
Vol 465 (2109) ◽  
pp. 2813-2823 ◽  
Author(s):  
A. Hiscox ◽  
B. M. Brown ◽  
M. Marletta
Keyword(s):  
Angular Momentum ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Large Radius ◽  
Complex Angular Momentum ◽  
Radial Schrödinger Equation ◽  
Generalized Complex ◽  
The Right ◽  
Math Phys ◽  
Regge Poles

We study the question addressed by Barut and Dilley ( Barut & Dilley 1963 J. Math. Phys . 4 , 1401–1408) of counting the number of Regge poles for a radial Schrödinger equation. Using the asymptotics of Rudolph Langer, we acquire estimates for the free solutions at infinity for large generalized complex angular momentum | λ |. These estimates allow us to calculate the Wronskian of two particular solutions, which is the function whose zeros are the Regge poles, for large | λ | in the right-half λ -plane. These angular momentum asymptotics are rigorously related to the large-radius asymptotics by generalizing Marianna Shubova’s idea of formulating an integral equation for the solution at infinity. This leads to the proof that for integrable potentials there are only finitely many Regge poles. This should be compared with the ideas of Barut and Dilley, who require that the potential be analytic in the right-half plane with r 2 V ( r ) remaining bounded.

scholarly journals Bound State Solutions of the Hua Potential within the Framework of Two Approximations Scheme

2021 ◽  
Vol 3 (3) ◽  
pp. 38-41
Author(s):  
E. B. Ettah ◽  
P. O. Ushie ◽  
C. M. Ekpo
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Equation ◽  
Bound State ◽  
S Wave ◽  
Angular Momenta ◽  
Special Cases ◽  
Uvarov Method

In this paper, we solve analytically the Schrodinger equation for s-wave and arbitrary angular momenta with the Hua potential is investigated respectively. The wave function as well as energy equation are obtained in an exact analytical manner via the Nikiforov Uvarov method using two approximations scheme. Some special cases of this potentials are also studied.

scholarly journals Calculation of Binding Energy and Wave Function for Exotic Hidden-Charm Pentaquark

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
F. Chezani Sharahi ◽  
M. Monemzadeh
Keyword(s):  
Wave Function ◽  
Binding Energy ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound State ◽  
The Other

In this study, pentaquark P c 4380 composed of a baryon Σ c , and a D ¯ ∗ meson is considered. Pentaquark is as a bound state of two-body systems composed of a baryon and a meson. The calculated potential will be expanded and replaced in the Schrödinger equation until tenth sentences of expansion. Solving the Schrödinger equation with the expanded potential of Pentaquark leads to an analytically complete approach. As a consequence, the binding energy E B of pentaquark P c and wave function is obtained. The results E B will be presented in the form of tables so that we can review the existence of pentaquark P c . Then, the wave function will be shown on diagrams. Finally, the calculated results are compared with the other obtained results, and the mass of observing pentaquark P c and the radius of pentaquark are estimated.

scholarly journals Solution of Schrödinger equation by Laplace transform

1968 ◽  
Vol 8 (3) ◽  
pp. 557-567 ◽  
Author(s):  
M. J. Englefield
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Laplace Transform ◽  
Schrodinger Equation ◽  
Bound State ◽  
Transform Method ◽  
The Laplace Transform ◽  
Scattering Phase ◽  
Straightforward Solution ◽  
The Fourier Transform

Laplace transform techniques for solving differential equations do not seem to have been directly applied to the Schrödinger equation in quantum mechanics. This may be because the Laplace transform of a wave function, in contrast to the Fourier transform, has no direct physical significance. However, this paper will show that scattering phase shifts and bound state energies can be determined from the singularities of the Laplace transform of the wave function. The Laplace transform method can thereby simplify calculations if the potential allows a straightforward solution of the transformed Schrödinger equation. Suitable cases are the Coulomb, oscillator and exponential potentials and the Yamaguchi separable non-local potential.

scholarly journals ANALYTICAL SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH THE WOODS–SAXON POTENTIAL FOR ARBITRARY l STATE

2009 ◽  
Vol 18 (03) ◽  
pp. 631-641 ◽  
Author(s):  
V. H. BADALOV ◽  
H. I. AHMADOV ◽  
A. I. AHMADOV
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
State Energy ◽  
Bound State ◽  
Saxon Potential ◽  
Energy Eigenvalues ◽  
Quantum Numbers ◽  
Radial Schrödinger Equation ◽  
Uvarov Method ◽  
Pekeris Approximation

In this work, the analytical solution of the radial Schrödinger equation for the Woods–Saxon potential is presented. In our calculations, we have applied the Nikiforov–Uvarov method by using the Pekeris approximation to the centrifugal potential for arbitrary l states. The bound state energy eigenvalues and corresponding eigenfunctions are obtained for various values of n and l quantum numbers.

scholarly journals Exact Analytical Solution of theN-Dimensional Radial Schrödinger Equation with Pseudoharmonic Potential via Laplace Transform Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Tapas Das ◽  
Altuğ Arda
Keyword(s):  
Schrödinger Equation ◽  
Laplace Transform ◽  
Schrodinger Equation ◽  
Exact Analytical Solution ◽  
Bound State ◽  
Pseudoharmonic Potential ◽  
Special Cases ◽  
Radial Schrödinger Equation ◽  
The Laplace Transform ◽  
Generalized Morse Potential

The second-orderN-dimensional Schrödinger equation with pseudoharmonic potential is reduced to a first-order differential equation by using the Laplace transform approach and exact bound state solutions are obtained using convolution theorem. Some special cases are verified and variations of energy eigenvaluesEnas a function of dimensionNare furnished. To give an extra depth of this paper, the present approach is also briefly investigated for generalized Morse potential as an example.

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