Bound State Wave Functions Through the Quantum Hamilton–jacobi Formalism

Ranjani, S. Sree; Geojo, K G; Kapoor, A. K.; Panigrahi, Prasanta K.

doi:10.1142/s0217732304013799

Cited by 50 publications

(71 citation statements)

References 28 publications

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“…Even though this approach appears similar to the familiar WKB scheme, it is worth pointing out that Eq. (13) reproduces the exact quantized energy eigenvalues [10]. Let us now apply the above formalism of quantum cosmology, as an example, to the flat FLRW minisuperspace model with perfect fluid as the matter field.…”

Section: Introductionmentioning

confidence: 90%

Quantum Hamilton-Jacobi Cosmology and Classical-Quantum Correlation

Fathi

Jalalzadeh

2017

Int J Theor Phys

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How the time evolution which is typical for classical cosmology emerges from quantum cosmology? The answer is not trivial because the Wheeler-DeWitt equation is time independent. A framework associating the quantum Hamilton-Jacobi to the minisuperspace cosmological models has been introduced in [1]. In this paper we show that time dependence and quantum-classical correspondence both arise naturally in the quantum Hamilton-Jacobi formalism of quantum mechanics, applied to quantum cosmology. We study the quantum Hamilton-Jacobi cosmology of spatially flat homogeneous and isotropic early universe whose matter content is a perfect fluid. The classical cosmology emerge around one Planck time where its linear size is around a few millimeter, without needing any classical inflationary phase afterwards to make it grow to its present size.

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Section: Introductionmentioning

confidence: 90%

Quantum Hamilton-Jacobi Cosmology and Classical-Quantum Correlation

Fathi

Jalalzadeh

2017

Int J Theor Phys

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“…From the above equation we can see that q ℓ has a simple pole at the origin along with 2ℓ fixed poles corresponding to the zeros of ξ ℓ (x 2 ; g). An important feature of all known ES models studied has been that the point at infinity is an isolated singularity [10]. The consequence of this is that the QMF has finite number of moving poles.…”

Section: Deformed Radial Oscillator Potentialsmentioning

confidence: 99%

Exceptional orthogonal polynomials, QHJ formalism and SWKB quantization condition

Ranjani¹,

Panigrahi²,

Khare³

et al. 2012

J. Phys. A: Math. Theor.

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We study the quantum Hamilton-Jacobi (QHJ) equation of the recently obtained exactly solvable models, related to the newly discovered exceptional polynomials and show that the QHJ formalism reproduces the exact eigenvalues and the eigenfunctions. The fact that the eigenfunctions have zeros and poles in complex locations leads to an unconventional singularity structure of the quantum momentum function p(x), the logarithmic derivative of the wave function, which forms the crux of the QHJ approach to quantization. A comparison of the singularity structure for these systems with the known exactly solvable and quasi-exactly solvable models reveals interesting differences. We find that the singularity structure of the momentum function for these new potentials lies between the above two distinct models, sharing similarities with both of them. This prompted us to examine the exactness of the supersymmetric WKB (SWKB) quantization condition. The interesting singularity structure of p(x) and of the superpotential for these models has important consequences for the SWKB rule and in our proof of its exactness for these quantal systems.

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“…The advantage of this method is that it is possible to determine the energy eigenvalues without having to solve for the eigenfunctions. In this formalism, singularity structure of the quantum momentum function There is a boundary condition in the limit QMF which is used to determine physically acceptable solutions for the QMF [29][30][31][32][33][34][35][36][37]. In the applications, Ranjani and her collaborators applied the QHJ formalism, to Hamiltonians with Khare-Mandal potential and Scarf potential, characterized by discrete parity and time reversal (PT) symmetries [31].…”

Section: Introductionmentioning

confidence: 99%