Do the generalized Fock-state wave functions have some relations with classical initial condition?

Choi, Jeong Ryeol; Yeon, Kyu-Hwang; Nahm, In Hyun; Kim, Seok Seong

doi:10.1007/s12043-009-0150-4

Cited by 3 publications

(3 citation statements)

References 15 publications

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“…By inserting the Hamiltonian into this equation, we derive a quadratic invariant operator as where f ( t ) is a time function that yields the nonlinear equation 21 , 33 …”

Section: Resultsmentioning

confidence: 99%

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Analysis of light-wave nonstaticity in the coherent state

Choi

2021

Sci Rep

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The characteristics of nonstatic quantum light waves in the coherent state in a static environment is investigated. It is shown that the shape of the wave varies periodically as a manifestation of its peculiar properties of nonstaticity like the case of the Fock-state analysis for a nonstatic wave. A belly occurs in the graphic of wave evolution whenever the wave is maximally displaced in the quadrature space, whereas a node takes place every time the wave passes the equilibrium point during its oscillation. In this way, a belly and a node appear in turn successively. Whereas this change of wave profile is accompanied by the periodic variation of electric and magnetic energies, the total energy is conserved. The fluctuations of quadratures also vary in a regular manner according to the wave transformation in time. While the resultant time-varying uncertainty product is always larger than (or, at least, equal to) its quantum-mechanically allowed minimal value ($$\hbar /2$$ ħ / 2 ), it is smallest whenever the wave constitutes a belly or a node. The mechanism underlying the abnormal features of nonstatic light waves demonstrated here can be interpreted by the rotation of the squeezed-shape contour of the Wigner distribution function in phase space.

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“…By inserting the Hamiltonian into this equation, we derive a quadratic invariant operator as where f ( t ) is a time function that yields the nonlinear equation 21 , 33 …”

Section: Resultsmentioning

confidence: 99%

“…At this stage, we introduce an annihilation operator associated with the invariant, Eq. ( 2 ), which is of the form 33 …”

Section: Resultsmentioning

confidence: 99%

Analysis of light-wave nonstaticity in the coherent state

Choi

2021

Sci Rep

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“…A quadratic invariant operator which follows the Liouville-von Neumann equation will be adopted for this purpose. Lots of dynamical properties of non-ideal physical systems including nonstatic light waves can be treated by means of such a dynamical invariant [32][33][34]. The reason why the invariant operator method is useful in this context is that a generalized quantum wave function of a light wave is obtained by utilizing an invariant operator instead of the direct use of the Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

Analysis of light-wave nonstaticity in the coherent state

Choi¹

2021

Preprint

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The characteristics of nonstatic quantum light waves in the coherent state in a static environment is investigated. It is shown that the shape of the wave varies periodically as a manifestation of its peculiar properties of nonstaticity like the case of the Fock-state analysis for a nonstatic wave.A belly occurs in the graphic of wave evolution whenever the wave is maximally displaced in the quadrature space, whereas a node takes place every time the wave passes the equilibrium point during its oscillation. In this way, a belly and a node appear in turn successively. Whereas this change of wave profile is accompanied by the periodic variation of electric and magnetic energies, the total energy is conserved. The fluctuations of quadratures also vary in a regular manner according to the wave transformation in time. While the resultant time-varying uncertainty product is always larger than (or, at least, equal to) its quantum-mechanically allowed minimal value (h/2), it is smallest whenever the wave constitutes a belly or a node. The mechanism underlying the abnormal features of nonstatic light waves demonstrated here can be interpreted by the rotation of the squeezed-shape contour of the Wigner distribution function in phase space.

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On the possible emergence of nonstatic quantum waves in a static environment

Choi

2021

Nonlinear Dyn

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Do the generalized Fock-state wave functions have some relations with classical initial condition?

Abstract: We examine whether the general type Fock-state wave functions for the harmonic oscillator have some relations with the classical initial condition.

Cited by 3 publications

References 15 publications

Analysis of light-wave nonstaticity in the coherent state

Analysis of light-wave nonstaticity in the coherent state

Analysis of light-wave nonstaticity in the coherent state

On the possible emergence of nonstatic quantum waves in a static environment

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