Functional representations in non-Fourier basis with applications

Pathak, R.K.; Chandra, Abhijit; Bhattacharyya, Krishnendu

doi:10.1103/physreva.48.4097

Cited by 23 publications

(18 citation statements)

References 24 publications

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“…Behavior of energy eigenvalues and certain properties will concern us here. Numerical results, wherever necessary for comparison, are either taken directly from the works cited above [10,11] or computed by employing the PB bases [12].…”

Section: Resultsmentioning

confidence: 99%

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Bound states of oscillators in infinite and finite domains: A semiclassical study

Mukhopadhyay

Bhattacharyya

2001

Int J of Quantum Chemistry

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ABSTRACT:By involving the uncertainty product along with a semiclassical requirement for observables, a simple variational scheme is employed to extract major features of bound states of systems in (−∞, ∞) and the same of systems confined in (−L, L). Special attention is paid to perturbative studies on the asymptotic behavior of energies for oscillators in infinite domains and dependence of energy spectra of oscillators in finite domains on various system parameters. A corrected form of the virial theorem is obtained in the latter case. The governing equations for quantum isothermal and adiabatic processes, derived recently, are also shown to be modified for general confined oscillator systems and closed-form expressions are found. These results are useful in dealing with the quantum Carnot cycles. Advantages of the present route over other semiclassical strategies are stressed. Pilot calculations demonstrate nicely the efficacy of the endeavor under various situations.

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Section: Resultsmentioning

confidence: 99%

“…Hence, energies given by the right-hand sides (rhs) of (8) and (10) [or (12)] are lower bounds to actual energies. This character is fortunately preserved even if we employ the known bound (2) to A n .…”

Section: Case A: X ∈ (−∞ ∞)mentioning

confidence: 99%

Bound states of oscillators in infinite and finite domains: A semiclassical study

Mukhopadhyay

Bhattacharyya

2001

Int J of Quantum Chemistry

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“…Then, from (8) and (12), we see that the ground eigenenergy state, e.g., of H(zP3l2, l), should obey in the limit z -co. Table IV shows how nicely our variational results for EO satisfies (14). This demonstration serves at least three purposes, viz.…”

Section: E N ( -) ] Is Next Found From (9)mentioning

confidence: 86%

“…This provides a motivation for employing alternative basis functions in the course of solving the DWP problem variationally. To this end, here we use the particle-in-a-box (PB) bases [14] and adopt a coupled linear-nonlinear variational strategy, in view of the remarkable performance of this recipe for the quartic anharmonic oscillator problem over the entire coupling range. However, obtaining good-quality results of eigenenergies is not the sole purpose of the present communication.…”

Section: Introductionmentioning

confidence: 99%

Eigenstates of double wells at varying well depths

Pathak

Bhattacharyya

1995

Int J of Quantum Chemistry

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mA recipe for the accurate calculation of eigenstates of quartic double-well oscillators is presented. The behavior of eigenenergies as a function of the coupling strength is also studied. The quality of the semiclassical (WKB) expression for eigenvalues is critically assessed in this context. The analysis also includes a discussion on the possibility of degeneracy in such one-dimensional systems. 0

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“…The results are obtained via a coupled variational strategy [26] that is capable of yielding high-quality data. The last entry in Table I shows values of (n) that have been computed directly.…”

Section: Resultsmentioning

confidence: 99%