Critical parameters and spherical confinement of H atom in screened Coulomb potential

Roy, Amlan K.

doi:10.1002/qua.25108

Cited by 50 publications

(61 citation statements)

References 68 publications

(129 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this work, generalized pseudospectral (GPS) method has been applied to compute E n,l of CHA. This method has produced very accurate results for various model and real systems including atoms and molecules in the last decade; some of which could be found in the references [32][33][34][35].…”

Section: Methodsmentioning

confidence: 99%

Fisher information in confined hydrogen-like ions

Mukherjee¹,

Majumdar²,

Roy³

2018

Chemical Physics Letters

Self Cite

View full text Add to dashboard Cite

Section: Methodsmentioning

confidence: 99%

Fisher information in confined hydrogen-like ions

Mukherjee¹,

Majumdar²,

Roy³

2018

Chemical Physics Letters

Self Cite

View full text Add to dashboard Cite

“…Note that, for construction of exact wave function of CHA for a specific state, one needs to provide the energy eigenvalue of that state. In our present calculation, E n,l of CHA are computed by invoking the GPS [23] method. This is applied, because in this pursuit, we are interested in the information measures in CHA, for which GPS energies have been found to be sufficiently accurate to provide correct eigenvalues and eigenfunctions.…”

Section: Theoretical Methodsmentioning

confidence: 99%

“…Many interesting aspects such as rearrangement and redistribution of ground and excited energy states, simultaneous and incidental degeneracy, change in hyperfine splitting constant as well as dipole shielding factor, nuclear magnetic screening constant, pressure, variation of static and dynamic polarizability, hyperpolarizability, information entropy, etc., were probed with varying confining radius (r c ). A vast literature exists on the subject; here we refer to a selective set [13][14][15][16][17][18][19][20][21][22][23][24]. Eigenvalues and eigenfunctions of CHA can be solved exactly in terms of Kummer M-function (confluent hypergeometric) [17].In past twenty years, information measures were explored extensively for various quantum systems in both free and confinement situations.…”

mentioning

confidence: 99%

Information-entropic measures for non-zero l states of confined hydrogen-like ions

Mukherjee

Roy

2018

Eur. Phys. J. D

Self Cite

View full text Add to dashboard Cite

Rényi entropy (R), Tsallis entropy (T ), Shannon entropy (S), and Onicescu energy (E) are studied in a spherically confined H atom (CHA), in conjugate space, with special emphasis on non-zero l states. This work is a continuation of our recently published work [1]. Representative calculations are done by employing exact analytical wave functions in r space. Accurate p space-wave functions are generated numerically by performing Fourier transform on respective r-space counterparts.Further, these are extended for H-isoelectronic series by applying the scaling relations. R, T are evaluated by choosing the order of entropic moments (α, β) as ( 3 5 , 3) in r and p spaces. Detailed, systematic results of all these measures with respect to variations of confinement radius r c are offered here for arbitrary n, l quantum numbers. For a given n, at small r c , R α r , T α r , S r collapse with rise of l, attain a minimum, then again grow up. Growth in r c shifts the point of inflection towards higher l values. An increase in Z enhances localization of a particular state. Several other new interesting inferences are uncovered. Comparison with literature results (available only for S in 2p, 3d states), offers excellent agreement. Confinement of an atom or molecule inside an impenetrable cavity was first studied in the fourth decade of twentieth century [2]. Progress of research on such quantum systems was reviewed several times [2-5] recording their importance in both fundamental physics and chemistry as well as in various engineering branches. They have relevance in many different physical situations, e.g., atoms under plasma environment, impurities in crystal lattice and semiconductor materials, trapping of atoms/molecules in zeolite cages or inside an endohedral cobweb of fullerenes, quantum wells, quantum wires, quantum dots [6] and so forth. Furthermore, such models were designed to mimic the high pressure environment inside the core of planets. Also, they have contemporary significance in interpreting various astrophysical phenomena [7] and many other interesting areas.Theoretical study of a Hydrogen atom within an infinite spherical cavity was first published in 1937 [8]. Over the years, this simple confined hydrogen atom (CHA) model has served as a precursor to improve our understanding about the consequences of confinement in atomic electronic structure. In last decade, a CHA under the influence of various restricted environment has been extensively followed. Majority of these investigations include trapping of H atom either in a spherical box of penetrable, impenetrable walls or inside a hard box of different geometrical shape and size [5,[9][10][11][12]. In the realm of atomic physics, CHA provides us with many attractive physical and chemical properties. Numerous theoretical methods like perturbation theory, Padé approximation, WKB method, Hypervirial theorem, power-series solution, Lie algebra, Lagrange-mesh method, asymptotic iteration method, generalized pseudo-spectral (GPS) method were invoked for their prop...

show abstract

“…In this work, generalized pseudospectral (GPS) method was employed to calculate E n,l of these states. This method has provided very accurate results for various model and real systems including atoms, molecules, some of which could be found in the references [40][41][42]. This is very well documented and therefore omitted here.…”

Section: Methodsmentioning

confidence: 98%

Some complexity measures in confined isotropic harmonic oscillator

Mukherjee

Roy

2019

J Math Chem

Self Cite

View full text Add to dashboard Cite

Various well-known statistical measures like López-Ruiz, Mancini, Calbet (LMC) and Fisher-Shannon complexity have been explored for confined isotropic harmonic oscillator (CHO) in composite position (r) and momentum (p) spaces. To get a deeper insight about CHO, a more generalized form of these quantities with Rényi entropy (R) is invoked here. The importance of scaling parameter in the exponential part is also investigated. R is estimated considering order of entropic moments α, β as ( 2 3 , 3) in r and p spaces respectively. Explicit results of these measures with respect to variation of confinement radius r c is provided systematically for first eight energy states, namely, 1s, 1p, 1d, 2s, 1f, 2p, 1g and 2d. Detailed analysis of these complexity measures provides many hitherto unreported interesting features.

show abstract

Critical parameters and spherical confinement of H atom in screened Coulomb potential

Cited by 50 publications

References 68 publications

Fisher information in confined hydrogen-like ions

Fisher information in confined hydrogen-like ions

Information-entropic measures for non-zero l states of confined hydrogen-like ions

Some complexity measures in confined isotropic harmonic oscillator

Contact Info

Product

Resources

About