Hamilton-Jacobi/action-angle quantum mechanics

Leacock, Robert A.; Padgett, Michael J.

doi:10.1103/physrevd.28.2491

Cited by 143 publications

(181 citation statements)

References 15 publications

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“…From the variational analysis [26][27][28][29], we can see that action S Ldt   satisfies: (4), (10) for the scalar potential  the ratios similar to (15), are correct: …”

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confidence: 99%

Riemann surface and quantization

2017

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This paper proposes an approach of the unified consideration of classical and quantum mechanics from the standpoint of the complex analysis effects. It turns out that quantization can be interpreted in terms of the Riemann surface corresponding to the multivalent Ln  function. A visual interpretation of «trajectories» of the quantum system and of the Feynman's path integral is presented. A magnetic dipole having a magnetic charge that satisfies the Dirac quantization rule was obtained.

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“…From the variational analysis [26][27][28][29], we can see that action S Ldt   satisfies: (4), (10) for the scalar potential  the ratios similar to (15), are correct: …”

mentioning

confidence: 99%

Riemann surface and quantization

2017

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“…Note that, the other value of λ, i.e., −a, when substituted instead of a+1 in (14), gives the QES condition for negative values of a, b i.e., for a → −a−1, b → −b−1…”

Section: Qes Condition and The Forms Of The Wave Functionsmentioning

confidence: 99%

“…In our earlier studies, we had looked at non-periodic ES, QES and ES periodic potentials through the QHJ formalism which was initiated by Leacock and Padgett [13,14]. We were successful in obtaining the quasi exact solvability condition [5] for QES models and in obtaining the eigenvalues and eigenfunctions for both the ES [15] and QES models [5].…”

Section: Introductionmentioning

confidence: 99%

Periodic Quasi-Exactly Solvable Models

2005

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Various quasi-exact solvability conditions, involving the parameters of the periodic associated Lamé potential, are shown to emerge naturally in the quantum Hamilton-Jacobi approach. It is found that, the intrinsic nonlinearity of the Riccati type quantum Hamilton-Jacobi equation is primarily responsible for the surprisingly large number of allowed solvability conditions in the associated Lamé case. We also study the singularity structure of the quantum momentum function, which yields the band edge eigenvalues and eigenfunctions. * akksprs@uohyd.ernet.in † akksp@uohyd.ernet.in ‡ prasanta@prl.ernet.in

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“…Within the Quantum Hamiltonian Jacobi approach (QHJ) [6][7], it has been found to be an elegant and the simple method to determine the energy spectrum of exactly solvable models in quantum mechanics. The advantage of this method is that it is possible to determine the energy eigen-values without having to solve for the eigen-functions.…”

Section: Introductionmentioning

confidence: 99%

“…In this formalism, a quantum analog of classical action angle variables is introduced [6][7] . The quantization condition represents well known results on the number nodes of the wave function, translated in terms of logarithmic derivative, also is called quantum momentum function (QMF) [3,[6][7]. The equation satisfied by the QMF is a non-linear differential equation, called quantum Hamilton-jacobi equation leads to two solutions.…”

Section: Introductionmentioning

confidence: 99%