Eigenstates of double wells at varying well depths

Pathak, R.K.; Bhattacharyya, Krishnendu

doi:10.1002/qua.560540104

Cited by 15 publications

(16 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…as basis set, in order to solve double-well potential and some other anharmonic symmetric oscillators [25,26,27,28]. They have shown that the trigonometric functions are a suitable basis-set in variational calculations in order to obtain highly accurate results.…”

Section: Introductionmentioning

confidence: 99%

Accurate energy spectrum for double-well potential: periodic basis

2010

View full text Add to dashboard Cite

We present a variational study of employing the trigonometric basis functions satisfying periodic boundary condition for the accurate calculation of eigenvalues and eigenfunctions of quartic double-well oscillators. Contrary to usual Dirichlet boundary condition, imposing periodic boundary condition on the basis functions results in the existence of an inflection point with vanishing curvature in the graph of the energy versus the domain of the variable. We show that this boundary condition results in a higher accuracy in comparison to Dirichlet boundary condition. This is due to the fact that the periodic basis functions are not necessarily forced to vanish at the boundaries and can properly fit themselves to the exact solutions.

show abstract

Section: Introductionmentioning

confidence: 99%

Accurate energy spectrum for double-well potential: periodic basis

2010

View full text Add to dashboard Cite

show abstract

“…At the same time such potentials are quite common for various problems encountered in physics and chemistry (see discussion in Ref. [35]).…”

Section: Double-well Oscillatorsmentioning

confidence: 99%

Self-similar interpolation in quantum mechanics

1998

View full text Add to dashboard Cite

An approach is developed for constructing simple analytical formulae accurately approximating solutions to eigenvalue problems of quantum mechanics. This approach is based on self-similar approximation theory. In order to derive interpolation formulae valid in the whole range of parameters of considered physical quantities, the self-similar renormalization procedure is complimented here by boundary conditions which define control functions guaranteeing correct asymptotic behaviour in the vicinity of boundary points. To emphasize the generality of the approach, it is illustrated by different problems that are typical for quantum mechanics, such as anharmonic oscillators, doublewell potentials, and quasiresonance models with quasistationary states. In addition, the nonlinear Schrödinger equation is considered, for which both eigenvalues and wave functions are constructed.02.30.Lt, 02.30.Mv, 03.65 Ge

show abstract

“…Apart from the basic physics of internal tunneling and doublet splitting, it has been used as testing grounds for different types of quantal or semiclassical treatments. Out of the plethora of such treatments, we glean a few 1–14.…”

Section: Introductionmentioning

confidence: 99%

Semiclassical path integral theory of a double‐well potential in an electric field

Douvropoulos

Nicolaides

2005

Int J of Quantum Chemistry

View full text Add to dashboard Cite

ABSTRACT:A recently published methodology based on semiclassical path integral (SCPI) theory was implemented in the case of a model of a double-well potential perturbed by a static electric field, with application to the inversion frequency of NH 3 . This model was chosen as an idealized case for testing of the present approach, as well as for quantum mechanical models that might be applied in the future. The calculations were concerned with the variation of the frequency of inversion as a function of field strength, F, and of distance, x f (from the symmetric point x o ϭ 0), where the field is "felt." It is found that this variation occurs sharply in very small regions of values of these parameters, and the system switches from internal oscillation to diffusion to the continuum. The fact that the theory is in analytic form allows the extraction of results and conclusions not only at the full SCPI level, but also at the Jeffreys-Wentzel-KramersBrillouin (JWKB) level. Comparison shows that the discrepancy sets in as the field strength increases, in accordance with the well-known limitations of the JWKB method regarding its dependence on the degree of variation of the potential as a function of position.

show abstract

Eigenstates of double wells at varying well depths

Cited by 15 publications

References 26 publications

Accurate energy spectrum for double-well potential: periodic basis

Accurate energy spectrum for double-well potential: periodic basis

Self-similar interpolation in quantum mechanics

Semiclassical path integral theory of a double‐well potential in an electric field

Contact Info

Product

Resources

About