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Exact Solutions of the Morse-like Potential,Step-Up and Step-Down Operators via Laplace Transform Approach

Altug, Arda, Ramazan +1 more

理论物理通讯：英文版Jan 1, 20121 citation

Solution of Schrödinger equation by Laplace transform

M. J. Englefield

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.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.

Journal of the Australian Mathematical SocietyAug 1, 196814 citations

Classical and Quantum Mechanics of Noncentral Potentials

R. S. Kaushal

Springer eBooksJan 1, 199836 citations

Exact Analytical Solution of the N -Dimensional Radial Schrödinger Equation with Pseudoharmonic Potential via Laplace Transform Approach

Tapas Das, Altuğ Arda

The second-order N -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 eigenvalues En as a function of dimension N are furnished. To give an extra depth of this paper, the present approach is also briefly investigated for generalized Morse potential as an example.

arXiv:1308.5295Advances in High Energy PhysicsJan 1, 201532 citations

Solution of the Schrödinger equation for a particular form of Morse potential using the Laplace transform

M. Zarezadeh, Mohammad Kazem Tavassoly

In this paper, we have solved the Schrödinger equation for a particular kind of Morse potential and find its normalized eigenfunctions and eigenvalues, exactly. Our work is based on the Laplace transform technique which reduces the second-order differential equation to a first-order.

Chinese Physics CApr 1, 201312 citations

Green's functions for separable potentials

S�ren Berg Padkj�r, Esper Dalgaard

Theoretical Chemistry AccountsDec 1, 19940 citations

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