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 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.

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 On solutions of local fractional Schrodinger equation

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 1929-1934
Author(s):  
Resat Yilmazer ◽  
Neslihan Demirel
Keyword(s):  
Fourier Transform ◽  
Schrödinger Equation ◽  
Laplace Transform ◽  
Closed Form ◽  
Schrodinger Equation ◽  
Fractional Schrödinger Equation ◽  
The Laplace Transform ◽  
Fractional Schrodinger Equation

In this study, we obtain the solution of a local fractional Schrodinger equation. The solution is obtained by the implementation of the Laplace transform and Fourier transform in closed form in terms of the Mittag-Leffler function.

Exact Solutions of the N-dimensional Radial Schrödinger Equation with the Coulomb Potential via the Laplace Tranform

2004 ◽  
Vol 59 (11) ◽  
pp. 875-876 ◽  
Author(s):  
Gang Chen
Keyword(s):  
Differential Equation ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Bound State ◽  
Factorization Approach ◽  
Exact Bound ◽  
Radial Schrödinger Equation ◽  
The Laplace Transform ◽  
03.65 Ge

The second-order N-dimensional Schrödinger differential equation with the Coulomb potential is reduced to a firstorder differential equation by means of the Laplace transform and the exact bound state solutions are obtained. It is shown that this method solving the Schrödinger equation may serve as a substitute for the factorization approach also in lower dimensions. - PACS numbers: 03.65.Ge.

scholarly journals Approximate Solutions of Schrodinger Equation with Some Diatomic Molecular Interactions Using Nikiforov-Uvarov Method

2017 ◽  
Vol 2017 ◽  
pp. 1-24 ◽  
Author(s):  
Ituen B. Okon ◽  
Oyebola Popoola ◽  
Cecilia N. Isonguyo
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Yukawa Potential ◽  
Diatomic Molecules ◽  
Bound State ◽  
Spectroscopic Constant ◽  
Expectation Values ◽  
Quadratic Potential ◽  
Uvarov Method

We used a tool of conventional Nikiforov-Uvarov method to determine bound state solutions of Schrodinger equation with quantum interaction potential called Hulthen-Yukawa inversely quadratic potential (HYIQP). We obtained the energy eigenvalues and the total normalized wave function. We employed Hellmann-Feynman Theorem (HFT) to compute expectation values r-2, r-1, T, and p2 for four different diatomic molecules: hydrogen molecule (H2), lithium hydride molecule (LiH), hydrogen chloride molecule (HCl), and carbon (II) oxide molecule. The resulting energy equation reduces to three well-known potentials which are as follows: Hulthen potential, Yukawa potential, and inversely quadratic potential. The bound state energies for Hulthen and Yukawa potentials agree with the result reported in existing literature. We obtained the numerical bound state energies of the expectation values by implementing MATLAB algorithm using experimentally determined spectroscopic constant for the different diatomic molecules. We developed mathematica programming to obtain wave function and probability density plots for different orbital angular quantum number.

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.

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