Generalized quantum similarity index: An application to pseudoharmonic oscillator with isospectral potentials in <scp>3D</scp>

Ghosh, Piu; Nath, Debraj

doi:10.1002/qua.26517

Cited by 12 publications

(31 citation statements)

References 127 publications

(173 reference statements)

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“…Let

f_{1} ((), r)

and

f_{2} ((), r)

be two radial density functions,

Ω_{r}^{1}

and

Ω_{r}^{2}

be the effective domains of

f_{1}

and

f_{2}

respectively with respect to

r

. Then

f_{1}

is called localized than

f_{2}

with respect to

r

normalℒ ((), {normalΩ}_{r}^{1}) < normalℒ ((), {normalΩ}_{r}^{2})

. Definition (Effective domain with respect to

θ

[37]). A region

Ω_{θ} \subset ([] 0, π)

is called the effective domain of the density function

f ((), θ)

, if

\int_{{normalΩ}_{θ}} f ((), θ) \sin θ italicdθ = 1

and there exists no

Ω_{1} \subset ([] 0, π)

such that

normalℒ ((), {normalΩ}_{1}) < normalℒ ((), {normalΩ}_{θ})

, where

\int_{{normalΩ}_{1}} f ((), θ) \sin θ italicdθ = 1

.…”

Section: Preliminaries About Density Functions and Rényi Entropymentioning

confidence: 99%

“…The harmonic spherical function is defined by [52]

Y_{normalℓ, m} ((),, θ, ϕ) = {[\frac{((), 2 normalℓ + 1) (()||, normalℓ -, m)!}{4 π (()||, normalℓ +, m)!}]}^{\frac{1}{2}} P_{ℓ}^{∣ m ∣} ((), \cos θ) e^{imϕ},

where

P_{ℓ}^{∣ m ∣} ((), \cos θ)

is the associate Legendre polynomial [75] of degree

normalℓ

\cos θ

and parameter

m

. On the other hand the wave solution and the ro‐vibrational energy of a family of isospectral potentials () are respectively [37, 49, 76, 77]

\begin{matrix} righttrue \\ {\overset{ψ}{true}}_{n, ℓ, m} (boldr, λ) = {\overset{C}{true}}_{n} \sqrt{Ω (r, λ)} {normalΦ}_{n} (r) Y_{ℓ, m} (θ, ϕ), \end{matrix}

and

{\overset{true^}{E}}_{n, normalℓ, m}^{3 D} = normalℏ ω_{r} ((), 4 n + 2 L + 3) - 2 D_{e},

where

\begin{matrix} lefttrue \\ Ω (r, λ) & = 2 <...> \end{matrix}

…”

Section: Applicationmentioning

confidence: 99%

“…Recently complexity ratio has been introduced in position and momentum spaces for radial pseudoharmonic oscillator potential [47]. With respect to generalized quantum similarity index [48], we already shown that, wave functions of some diatomic molecules are same for pseudoharmonic oscillator, which are matched with a family isospectral potentials in 3D [49].…”

Section: Introductionmentioning

confidence: 99%

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An introduction to analysis of Rényi complexity ratio of quantum states for central potential

Nath

2021

Int J of Quantum Chemistry

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Rényi complexity ratio of two density functions is introduced for three and multidimensional quantum systems. Localization property of several density functions are defined and five theorems about near continuous property of Rényi complexity ratio are proved by Lebesgue measure. Some properties of Rényi complexity ratio are demonstrated and investigated for different quantum systems. Exact analytical forms of Rényi entropy, Rényi complexity ratio, statistical complexities based on Rényi entropy for integral order have been presented for solutions of pseudoharmonic and a family of isospectral potentials. Some properties of Rényi complexity ratio are verified for six diatomic molecules (CO, NO, N2, CH, H2, and ScH) and for other quantum systems.

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“…Let

f_{1} ((), r)

and

f_{2} ((), r)

be two radial density functions,

Ω_{r}^{1}

and

Ω_{r}^{2}

be the effective domains of

f_{1}

and

f_{2}

respectively with respect to

r

. Then

f_{1}

is called localized than

f_{2}

with respect to

r

normalℒ ((), {normalΩ}_{r}^{1}) < normalℒ ((), {normalΩ}_{r}^{2})

. Definition (Effective domain with respect to

θ

[37]). A region

Ω_{θ} \subset ([] 0, π)

is called the effective domain of the density function

f ((), θ)

, if

\int_{{normalΩ}_{θ}} f ((), θ) \sin θ italicdθ = 1

and there exists no

Ω_{1} \subset ([] 0, π)

such that

normalℒ ((), {normalΩ}_{1}) < normalℒ ((), {normalΩ}_{θ})

, where

\int_{{normalΩ}_{1}} f ((), θ) \sin θ italicdθ = 1

.…”

Section: Preliminaries About Density Functions and Rényi Entropymentioning

confidence: 99%

“…The harmonic spherical function is defined by [52]

Y_{normalℓ, m} ((),, θ, ϕ) = {[\frac{((), 2 normalℓ + 1) (()||, normalℓ -, m)!}{4 π (()||, normalℓ +, m)!}]}^{\frac{1}{2}} P_{ℓ}^{∣ m ∣} ((), \cos θ) e^{imϕ},

where

P_{ℓ}^{∣ m ∣} ((), \cos θ)

is the associate Legendre polynomial [75] of degree

normalℓ

\cos θ

and parameter

m

. On the other hand the wave solution and the ro‐vibrational energy of a family of isospectral potentials () are respectively [37, 49, 76, 77]

\begin{matrix} righttrue \\ {\overset{ψ}{true}}_{n, ℓ, m} (boldr, λ) = {\overset{C}{true}}_{n} \sqrt{Ω (r, λ)} {normalΦ}_{n} (r) Y_{ℓ, m} (θ, ϕ), \end{matrix}

and

{\overset{true^}{E}}_{n, normalℓ, m}^{3 D} = normalℏ ω_{r} ((), 4 n + 2 L + 3) - 2 D_{e},

where

\begin{matrix} lefttrue \\ Ω (r, λ) & = 2 <...> \end{matrix}

…”

Section: Applicationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An introduction to analysis of Rényi complexity ratio of quantum states for central potential

Nath

2021

Int J of Quantum Chemistry

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“…If wave functions of any one Hamiltonian H − (or H + ) are known, then one can obtain another set of wave functions for the Hamiltonian H + (or H − ), using super-symmetric quantum mechanics and they are obtained from [45,54,55,56,57]…”

Section: Construct To Solvable Time-dependent Potentials and Their Wa...mentioning

confidence: 99%

Comparison between time-independent and time-dependent quantum systems in the context of energy, Heisenberg uncertainty, average energy, force, average force and thermodynamic quantities

Nath¹

2021

Preprint

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Exact solutions of time-dependent Schrödinger equation in presence of time-dependent potential is defined by point transformation and separation of variables. Energy and Heisenberg uncertainty relation are pursued for timeindependent potential whereas average energy and Heisenberg uncertainty relation are defined for time-dependent potential. Forces acting on a fixed boundary wall as well as average force acting on moving boundary wall are presented along various trajectories. For high temperature, analytical forms of partition function and the corresponding thermodynamic quantities are derived following the Euler-Maclaurin summation formula over a finite as well as an infinite domain for accurate presentation. Three quantum systems are generated with the help of point transformation, separation of variables and super-symmetric quantum mechanics from one quantum system and the corresponding results are compared among all systems, where two of them are time-independent and another two are time-dependent.

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“…Moreover, we will define effective domain of continuous probability density function. Then characterize its localization property with respect to the effective domain [63,64]. Next, we will investigate the connection between the majorization and the localization property of continuous density functions.…”

mentioning

confidence: 99%

Majorization effect on entropic functionals: An application to a V-type three-level atom-field interacting system

Nath¹

2021

Preprint

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The majorization effect on some entropic functionals, such as von-Neumann, Shannon, atomic Wehrl and Rényi entropies are investigated of a vee type three-level atom which interacts with a coherent field in a resonant cavity.Moreover, the fidelity, purity and linear entropy are investigated of two quantum systems, which contain photon number distributions (discrete) and Husimi Q function (continuous distribution). A relation between the majorization and localization properties of continuous density functionals is established. The results are compared and verified for continuous and discrete distributions.

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Generalized quantum similarity index: An application to pseudoharmonic oscillator with isospectral potentials in 3D

Cited by 12 publications

References 127 publications

An introduction to analysis of Rényi complexity ratio of quantum states for central potential

An introduction to analysis of Rényi complexity ratio of quantum states for central potential

Comparison between time-independent and time-dependent quantum systems in the context of energy, Heisenberg uncertainty, average energy, force, average force and thermodynamic quantities

Majorization effect on entropic functionals: An application to a V-type three-level atom-field interacting system

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