Exact solution of the Schrödinger equation with a Lennard–Jones potential

Sesma, J.

doi:10.1007/s10910-013-0189-9

Cited by 8 publications

(5 citation statements)

References 19 publications

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“…The results of this paper illustrate the idea that only certain discrete values of external pressure can provoke excitation and ionisation at the atomic/molecular level thus leading to phase transitions at the "macroscopic"level. It is planned to perform a similar calculation for the Lennard -Jones potential, which is more realistic and for which the Schrödinger equation has been solved only recently [15].…”

Section: Discussionmentioning

confidence: 99%

A simple example of pressure excitation:the 3D square well potential

Celebonovic,

Nikolic

2016

Preprint

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High pressure experiments in diamond anvil cells as well as in geophysics show that at certain discrete values of pressure abrupt changes of the mass density and changes of the material structure occur. The aim of this paper is to discuss the influence of high external pressure on atoms and molecules using the 3D square well potential as a simple solvable quantum mechanical example. Values of external pressure needed for a transition between energy levels with different values of the main quantum number n, as well as the pressure needed to expel the particle from this system are calculated. In both cases discrete values of pressure are obtained.

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Section: Discussionmentioning

confidence: 99%

A simple example of pressure excitation:the 3D square well potential

Celebonovic,

Nikolic

2016

Preprint

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“…In the cases of the Kratzer and Morse potentials, the availability of exact solutions to their Schrödinger equations have also enhanced their applicability. [25][26][27][28][29] Generalizations and adaptions of these potentials have also lead to more sophisticated applications.…”

Section: Introductionmentioning

confidence: 99%

“…These three potentials have continued popularity for widespread applications, primarily because of limited numbers of adjustable parameters and their abilities to account for the most important inherent characteristics of the potentials that they are chosen to represent. In the cases of the Kratzer and Morse potentials, the availability of exact solutions to their Schrödinger equations have also enhanced their applicability. − Generalizations and adaptions of these potentials have also lead to more sophisticated applications.…”

Section: Introductionmentioning

confidence: 99%

Morse, Lennard-Jones, and Kratzer Potentials: A Canonical Perspective with Applications

et al. 2016

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Canonical approaches are applied to classic Morse, Lennard-Jones, and Kratzer potentials. Using the canonical transformation generated for the Morse potential as a reference, inverse transformations allow the accurate generation of the Born-Oppenheimer potential for the H ion, neutral covalently bound H, van der Waals bound Ar, and the hydrogen bonded one-dimensional dissociative coordinate in a water dimer. Similar transformations are also generated using the Lennard-Jones and Kratzer potentials as references. Following application of inverse transformations, vibrational eigenvalues generated from the Born-Oppenheimer potentials give significantly improved quantitative comparison with values determined from the original accurately known potentials. In addition, an algorithmic strategy based upon a canonical transformation to the dimensionless form applied to the force distribution associated with a potential is presented. The resulting canonical force distribution is employed to construct an algorithm for deriving accurate estimates for the dissociation energy, the maximum attractive force, and the internuclear separations corresponding to the maximum attractive force and the potential well.

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“…Our method to obtain such global solutions finds inspiration in a procedure proposed by Naundorf [20,21] forty years ago. The method, later considerably improved [22], has been used for the solution of several quantum problems [23,24,25]. For rational values a > 2 a general formalism can be written.…”

Section: Introductionmentioning

confidence: 99%

Scattering by infinitely rising one-dimensional potentials

Ferreira

Sesma

2015

Annals of Physics

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Infinitely rising one-dimensional potentials constitute impenetrable barriers which reflect totally any incident wave. However, the scattering by such kind of potentials is not structureless: resonances may occur for certain values of the energy. Here we consider the problem of scattering by the members of a family of potentials Va(x) = −sgn(x) |x| a , where sgn represents the sign function and a is a positive rational number. The scattering function and the phase shifts are obtained from global solutions of the Schrödinger equation. For the determination of the Gamow states, associated to resonances, we exploit their close relation with the eigenvalues of the PT -symmetric Hamiltonians with potentials V PT a (x) = −i sgn(x) |x| a . Calculation of the time delay in the scattering at real energies is used to characterize the resonances. As an additional result, the breakdown of the PT -symmetry of the family of potentials V PT a for a < 3 may be conjectured.

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Exact solution of the Schrödinger equation with a Lennard–Jones potential

Cited by 8 publications

References 19 publications

A simple example of pressure excitation:the 3D square well potential

A simple example of pressure excitation:the 3D square well potential

Morse, Lennard-Jones, and Kratzer Potentials: A Canonical Perspective with Applications

Scattering by infinitely rising one-dimensional potentials

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