Partner Potentials Research Articles

Infinite families of position-dependent mass Schrödinger equations with known ground and first excited states

A construction method of infinite families of quasi-exactly solvable position-dependent mass Schrödinger equations with known ground and first excited states is proposed in a deformed supersymmetric background. Such families correspond to extensions of known potentials endowed with a deformed shape invariance property. Two different approaches are combined. The first one is a generating function method, which enables to construct the first two superpotentials of a deformed supersymmetric hierarchy, as well as the first two partner potentials and the first two eigenstates of the first potential, from some generating function W+(x) [and its accompanying function W−(x)]. The second approach is the conditionally deformed shape invariance method, wherein the deformed shape invariance property of the starting potentials is generalized to their extensions by adding some constraints on the parameters and by imposing compatibility conditions between sets of constraints. Detailed results are given for some extensions of the linear and radial harmonic oscillators, as well as the Kepler–Coulomb and Morse potentials.

Generalized Lennard-Jones Potentials, SUSYQM and Differential Galois Theory

In this paper we start with proving that the Schr\"odinger equation (SE) with the classical $12-6$ Lennard-Jones (L-J) potential is nonintegrable in the sense of the differential Galois theory (DGT), for any value of energy; i.e., there are no solutions in closed form for such differential equation. We study the $10-6$ potential through DGT and SUSYQM; being it one of the two partner potentials built with a superpotential of the form $w(r)\propto 1/r^5$. We also find that it is integrable in the sense of DGT for zero energy. A first analysis of the applicability and physical consequences of the model is carried out in terms of the so called De Boer principle of corresponding states. A comparison of the second virial coefficient $B(T)$ for both potentials shows a good agreement for low temperatures. As a consequence of these results we propose the $10-6$ potential as an integrable alternative to be applied in further studies instead of the original $12-6$ L-J potential. Finally we study through DGT and SUSYQM the integrability of the SE with a generalized $(2\nu-2)-\nu$ L-J potential. This analysis do not include the study of square integrable wave functions, excited states and energies different than zero for the generalization of L-J potentials.

Deformed shape invariance symmetry and potentials in curved space with two known eigenstates

We consider two families of extensions of the oscillator in a d-dimensional constant-curvature space and analyze them in a deformed supersymmetric framework, wherein the starting oscillator is known to exhibit a deformed shape invariance property. We show that the first two members of each extension family are also endowed with such a property, provided some constraint conditions relating the potential parameters are satisfied, in other words they are conditionally deformed shape invariant. Since, in the second step of the construction of a partner potential hierarchy, the constraint conditions change, we impose compatibility conditions between the two sets to build potentials with known ground and first excited states. To extend such results to any members of the two families, we devise a general method wherein the first two superpotentials, the first two partner potentials, and the first two eigenstates of the starting potential are built from some generating function W+(r) [and its accompanying function W−(r)].

The solution of 4-dimensional Schrodinger equation for polynomial inverse potential and its partner potential by using ansatz wavefunction method

The radial part of 4-dimensional Schrodinger equation for Polynomial Inverse potential and its partner potential was solved by using the Ansatz Wavefunction method. By applying of the properties and operators of the Supersymmetric Quantum Mechanic method the partner potential was constructed. The eigenvalues and eigenfunctions of the Polynomial Inverse potential and the eigenvalues and eigenfunctions of its partner potential were different. The partner potential of Polynomial Inverse potential for n > 1 has eigenvalue greater than Polynomial Inverse potential as its original potential.

The construction of partner potential from the general potential anharmonic in D-dimensional Schrodinger system

The Schrodinger equation is the fundamental equation in quantum physics. The characteristic of the particle in physics potential field can be explained by using the Schrodinger equation. In this study, the solution of 4 dimensional Schrodinger equation for the anharmonic potential and the anharmonic partner potential have done. The method that used to solve the Schrodinger equation was the ansatz wave method, while to construction the partner potential was the supersymmetric method. The construction of partner potential used to explain the experiment result that cannot be explained by the original potential. The eigenvalue for anharmonic potential and the anharmonic partner potential have the same characteristic. Every increase of quantum orbital number the eigenvalue getting smaller. This result corresponds to Bohrn’s atomic theory that the eigenvalue is inversely proportional to the atomic shell. But the eigenvalue for the anharmonic partner potential higher than the eigenvalue for the anharmonic original potential.

SUSY Quantum Mechanics for PT Symmetric Systems

A new way of constructing SUSY partner potentials with PT symmetry is proposed. In this construction, PT symmetric superpotentials generate PT symmetric SUSY partners and supercharges that satisfy commutator-anti-commutator relations of close superalgebra SL(1/1). Conversely, every PT symmetric Hamiltonian having zero or non zero ground state energy can be generated using PT symmetric superpotentials. Further, superpotentials having separate P and T symmetries can generate strictly isospectral SUSY partners if the wedge of integration can accommodate two asymptotically opposite quantization contours.

Limits to networking capabilities: Relationship trade-offs and innovation

The capability of firms to leverage external network relationships strongly supports the development of successful new products and services. Network partners help to shape innovations and pave the road to commercialisation. Yet, despite this considerable knowledge about the importance of networks for innovation, we do not understand how firms embedded with multiple network partners manage competing priorities and associated attention trade-offs to maximise the full innovation potential of these relationships. Gaining insight into this deficit would serve to clarify networking capability theory and challenge its ‘more is better’ truism. To study this, we investigate Australian oil and gas firms' relationships with customers and suppliers, and trade-offs between these channels, to discover the impact upon innovation. We find that, while focused relationships within each channel (deep embeddedness) supports innovation, increasing vertical embeddedness with suppliers and customers simultaneously lowers firms' ability to introduce new products or services. Two findings emerge from our research: first, that there may be organisational limits to the attention span necessary to fully leverage the innovation potential of multiple network partners; and second that increasing vertical embeddedness may lock firms into non-innovative network positions. Findings indicate a strong need for attention-switching capabilities at the firm level.

The construction of partner potential from the general potential Rosen-Morse and Manning Rosen in 4 dimensional Schrodinger system

The solution of the Schrodinger equation with physical potential is the important part in quantum physics. Many methods have been developed to resolve the Schrodinger equation. The Nikiforov-Uvarov method and supersymmetric method are the most methods that interesting to be explored. The supersymmetric method not only used to solve the Schrodinger equation but also used to construct the partner potential from a general potential. In this study, the Nikiforov-Uvarov method was used to solve the Schrodinger equation while the supersymmetric method was used to construction partner potential. The study about the construction of the partner potential from general potential Rosen-Morse and Manning Rosen in D-dimensional Schrodinger system has been done. The partner potential was obtained are solvable. By using the Nikiforov-Uvarov method the eigenfunction of the Schrodinger equation in D-dimensional system with general potential Rosen-Morse and Manning Rosen and the Schrodinger equation in D-dimensional system with partner potential Rosen-Morse and Manning Rosen are determined. The eigenfunctions are different between the Schrodinger equation with general potential and the Schrodinger potential with the partner potential.

The solution of 4-dimensional Schrodinger equation for Scarf potential and its partner potential constructed By SUSY QM

The angular part of 4-dimensional Schrodinger equation for Scarf potential was solved by using the Nikiforov-Uvarov method and Supersymmetric Quantum Mechanic method. The determination of the ground state wave function has been used Nikiforov-Uvarov method and by applying the parametric generalization of the hypergeometric type equation. By using manipulation of the properties and operators of the Supersymmetric Quantum Mechanic method the partner potential was constructed. The ground state wave functions of original Scarf potential is different than the ground state wave functions of the construction result potential.

Constitutive calcium entry and cancer: updated views and insights.

Tight control of basal cytosolic Ca2+ concentration is essential for cell survival and to fine-tune Ca2+-dependent cell functions. A way to control this basal cytosolic Ca2+ concentration is to regulate membrane Ca2+ channels including store-operated Ca2+ channels and secondary messenger-operated channels linked to G-protein-coupled or tyrosine kinase receptor activation. Orai, with or without its reticular STIM partner and Transient Receptor Potential (TRP) proteins, were considered to be the main Ca2+ channels involved. It is well accepted that, in response to cell stimulation, opening of these Ca2+ channels contributes to Ca2+ entry and the transient increase in cytosolic Ca2+ concentration involved in intracellular signaling. However, in various experimental conditions, Ca2+ entry and/or Ca2+ currents can be recorded at rest, without application of any experimental stimulation. This led to the proposition that some plasma membrane Ca2+ channels are already open/activated in basal condition, contributing therefore to constitutive Ca2+ entry. This article focuses on direct and indirect observations supporting constitutive activity of channels belonging to the Orai and TRP families and on the mechanisms underlying their basal/constitutive activities.

Female factors infertility: Laparoscopic evaluation at a public health facility in Ilorin, Nigeria

Background: Infertility is a problem of global proportions, the majority being the residents of developing countries. The contribution of female factor is assuming a tremendous proportion. Laparoscopy remains an indispensable tool in the evaluation of the fertility potential of these female partners. Aims: This study was aimed at determining the various causes of female factor infertility among female partners of infertile couple in a tertiary health facility. Methods: A cross-sectional observational study of ninety seven (97) eligible infertile women who underwent diagnostic laparoscopy between 1st January 2012 and 31st December 2015 were enrolled for the study. The data were analyzed using SPSS/PC version 16.0 and p value was preset at Results: The patients aged 21-50 years with a mean age of 33.2 ± 6.6 years. Majority (79.4%) were nulliparous. Fifty (51.5%) had primary infertility. Their duration of infertility ranged from 1to 33years (5.7 ± 5.5 years). Most (63.9%) belong to middle social class and their spouse age ranges between 28-60 years (39.0 ± 7.5). More than a quarter had clomiphene resistant Polycystic Ovarian Syndrome, 19 (19.6%) tubal blockage, 13 (13.4%) uterine fibroid and 10 (10.3%) each had endometriosis, peritubal and ovarian adhesions, ovarian cyst and normal findings respectively. There was significant association between patients' age, intra-operative findings and tubal patency evaluation on laparoscopy (P Conclusion: Laparoscopic procedures are less invasive, more convenient and more precise for diagnosis of infertility in women. The common causes responsible for infertility were polycystic ovarian syndrome, tubal occlusion, uterine fibroid, endometriosis, peri-tubovarian adhesions and ovarian cyst.

Symbiotic Potential of Bradyrhizobium japonicum Strains with Different Growth Rates

To study genetic properties of soybean nodule bacteria with different growth rates, to research the ability of rhizobia to produce phytohormonal substances and estimate their symbiotic potential in the conditions of combined inoculation and mono-inoculation of soybean plants. Sequencing of the 16S-23S rDNA intergenic spacer of soybean rhizobia was performed on ABI 3130xl Genetic Analyzer. Determination of the qualitative and quantitative composition of phytohormones in culture liquid of Bradyrhizobium japonicum strains was performed by SDTLC-chromatography of high resolution. Symbiotic potential of the strains was estimated in the field experiment in Polissia area of Ukraine. It has been established that strains of soybean nodule bacteria with different growth rates by the structure of ITS region belong to different genetic groups: USDA 6, USDA 110 and USDA 123. The studied rhizobia differ in the levels of extracellular phytohormones synthesis: the slow-growing B. japonicum strain 46 produces more amounts of auxins, but the intensive-growing B. japonicum strain KB11 significantly exceeds in the amounts of cytokinins. It has been shown that an important factor of increasing soybean productivity is the formation of balanced symbiotic systems of the host plant with several complementary strains but serologically and genetically different strains of rhizobia of the same species. Combined inoculation of soybean seeds with two active strains B. japonicum 46 and B. japonicum KB11 allows more fully realizing the potential of symbiotic partners and receiving the higher yield.

SUSY method for the three-dimensional Schrödinger equation with effective mass

The three-dimensional Schrödinger equation with a position-dependent (effective) mass is studied in the framework of Supersymmetrical (SUSY) Quantum Mechanics. The general solution of SUSY intertwining relations with first order supercharges is obtained without any preliminary constraints. Several forms of coefficient functions of the supercharges are investigated and analytical expressions for the mass function and partner potentials are found. As usual for SUSY Quantum Mechanics with nonsingular superpotentials, the spectra of intertwined Hamiltonians coincide up to zero modes of supercharges, and the corresponding wave functions are connected by intertwining relations. All models are partially integrable by construction: each of them has at least one second order symmetry operator.

Parametric symmetries in exactly solvable real and PT symmetric complex potentials

In this paper, we discuss the parametric symmetries in different exactly solvable systems characterized by real or complex PT symmetric potentials. We focus our attention on the conventional potentials such as the generalized Pöschl Teller (GPT), Scarf-I, and PT symmetric Scarf-II which are invariant under certain parametric transformations. The resulting set of potentials is shown to yield a completely different behavior of the bound state solutions. Further, the supersymmetric partner potentials acquire different forms under such parametric transformations leading to new sets of exactly solvable real and PT symmetric complex potentials. These potentials are also observed to be shape invariant (SI) in nature. We subsequently take up a study of the newly discovered rationally extended SI potentials, corresponding to the above mentioned conventional potentials, whose bound state solutions are associated with the exceptional orthogonal polynomials (EOPs). We discuss the transformations of the corresponding Casimir operator employing the properties of the so(2, 1) algebra.

THE POSITIVE POTENTIAL OF THE ORGANISATION AND KNOWLEDGE PARTNERING

Purpose: Identify the key elements of the concept of Positive Potential of the Organisation (PPO) and provide the answer to the question whether the use of knowledge partnering can enhance the PPO. Approach: This is a literature and research review paper. Findings: The paper highlights the important role of knowledge partnering in the process of developing and strengthening the positive potential of modern organisations based on the example of high-tech enterprises operating in Poland. It can be noted that the analysed companies develop intraorganisational knowledge partnering significantly more often than inter-organisational knowledge partnering. At the same time, it has been shown that personalised knowledge is valued most by this kind of entities. Contacts with other partners from the business environment (customers, suppliers, etc.) are also highly valued. These factors exert a somewhat stronger influence on the development and the positive potential of high-tech medium and large enterprises and have a weaker impact on small enterprises. Although small high-tech enterprises need most the support flowing from the positive potential of knowledge partnering, in practice they still receive it to the smallest extent. In general, for the high-tech companies surveyed, knowledge partnering is to a large extent a real stimulus for market operations, as well as a catalyst for even the most difficult forms of cooperation, which means it can be considered as an important source of positive potential. Implications: The study shows the need for integration of knowledge partnering practices and positive potential management. The study indicates that knowledge partnering creates growth of positive organisational potential. Originality/value of the paper: The study suggests that well-developed processes of knowledge partnering stimulate competitive activities and the positive potential of not only large and mediumsized enterprises but also small ones.

Gazeau-Klauder coherent states for the partner potentials of the trigonometric symmetric scarf type

The supersymmetric partner Schrodinger equations for the superpotential $-A\tan\theta$ with A as non-negative integers are solved by using the Darboux factorization method on the associated Romanovski differential equation. The bound states correspond to a particle which is trapped on the bounded interval $-\pi/2\leq\theta\leq +\pi/2$ and their number is infinite. Its partner Hamiltonians are iso-spectral except for the ground state which, in turn, leads us to associate different Gazeau-Klauder coherent states for each of the partner potentials with different positive definite measures to realize the resolution of identity condition. It is shown that the time evolution does not change the form of the Gazeau-Klauder coherent states. Furthermore, it is discussed that the weight distribution functions of each of the coherent states obey the sub-Poissonian statistics. Finally, Gazeau-Klauder cat states are introduced for one of the partner potentials.

Determinants of infertility in male partners of infertile couples at a public health facility in Ilorin, Nigeria

Background: Infertility is the most important reproductive health and social issue confronting married couples in our environment. The contribution of male factor is assuming a tremendous proportion. Seminal fluid analysis (SFA) remains an indispensable tool in the evaluation of the fertility potential of these male partners. Aim and Objectives: This study aimed to determine the pattern of seminal fluid parameters and its impact on infertility among male partners of infertile couple at a public health facility in Ilorin. Materials and Methods: A cross-sectional study of the seminal fluid indices of consecutively consenting male partners of infertile couple seen at the Assisted Reproductive Technology (ART) Unit of the Department of Obstetrics Gynecology, University of Ilorin Teaching Hospital, Ilorin, between January 1, 2012 and December 31, 2014. Results: All male partners of infertile couple who had infertility consultation at the ART unit consented to SFA during the study period. The patients were aged 27-67 years. One hundred and seventy-five (56.1%) patients had normal parameters. There was a high level of leukocytospermia and bacterial infections in both normospermic and oligospermic semen. The predominant organism was Staphylococcus aureus. Of the sociodemographic and reproductive/hormonal variables, only the age was found to have statistically significant association with types of infertility. Conclusion: Male factor is increasingly assuming a significant role in the etiology of infertility in Ilorin. The practitioners should, therefore, endeavor to involve them early in the overall management to reduce stigmatization and ostracizing of women for infertility.

Normal ordering for nonlinear deformed ladder operators and the f-generalization of the Stirling and Bell numbers

We resolve the normal ordering problem for symmetric (Dˆ+Dˆ−)n and asymmetric (Dˆ+rDˆ−)n strings of the nonlinear deformed ladder operators Dˆ± for supersymmetric and shape-invariant potential systems, where r and n are positive integers. We provide exact and explicit expressions for their normal forms N{(Dˆ+Dˆ−)n} and N{(Dˆ+rDˆ−)n}, where in N{...} all Dˆ− are at the right side. We find that the solutions involve sequence of expansion coefficients which, for r, n > 1, corresponds to the f-deformed generalization of the classical Stirling and Bell numbers of the second kind. We apply the general formalism for the translational shape-invariant potential systems as well as for the particular case of the harmonic oscillator potential system. We show that these numbers are obtained for families of polynomial expressions generated with the deformations parameters and the parameters related to the forms of the supersymmetric partner potentials.

Separable wave equations for gravitoelectromagnetic perturbations of rotating charged black strings

Rotating charged black strings are exact solutions of four-dimensional Einstein–Maxwell equations with a negative cosmological constant and a non-trivial spacetime topology. According to the AdS/CFT correspondence, these black strings are dual to rotating thermal states of a strongly interacting quantum field theory with nonzero chemical potential that lives in a cylinder. The dynamics of linear fluctuations in the dual field theory can be studied from the perturbation equations for classical fields in a black-string spacetime. With this motivation in mind, we develop here a completely gauge and tetrad invariant perturbation approach to deal with the gravitoelectromagnetic fluctuations of rotating charged black strings in the presence of sources. As usual, for any charged black hole, a perturbation in the background electromagnetic field induces a metric perturbation and vice versa. In spite of this coupling and the non-vanishing angular momentum, we show that linearization of equations of the Newman–Penrose formalism leads to four separated second-order complex equations for suitable combinations of the spin coefficients, the Weyl and the Maxwell scalars. Then, we generalize the Chandrasekhar transformation theory by the inclusion of sources and apply it to reduce the perturbation problem to four decoupled inhomogeneous wave equations—a pair for each sector of perturbations. The radial part of such wave equations can be put into Schrödinger-like forms after Fourier transforming them with respect to time. We find that the resulting effective potentials form two pairs of supersymmetric partner potentials and, as a consequence, the fundamental variables of one perturbation sector are related to the variables of the other sector. The relevance of such a symmetry in connection to the AdS/CFT correspondence is discussed, and future applications of the pertubation theory developed here are outlined.

Interplay between parity-time symmetry, supersymmetry, and nonlinearity: An analytically tractable case example.

In the present work, we combine the notion of parity-time (PT) symmetry with that of supersymmetry (SUSY) for a prototypical case example with a complex potential that is related by SUSY to the so-called Pöschl-Teller potential which is real. Not only are we able to identify and numerically confirm the eigenvalues of the relevant problem, but we also show that the corresponding nonlinear problem, in the presence of an arbitrary power-law nonlinearity, has an exact bright soliton solution that can be analytically identified and has intriguing stability properties, such as an oscillatory instability, which is absent for the corresponding solution of the regular nonlinear Schrödinger equation with arbitrary power-law nonlinearity. The spectral properties and dynamical implications of this instability are examined. We believe that these findings may pave the way toward initiating a fruitful interplay between the notions of PT symmetry, supersymmetric partner potentials, and nonlinear interactions.