Search or ask a question

Why use makarov potential in solving schrodinger equation? what is reaaly the uses of a makarov potential?

Partition function (statistical mechanics)

Entropy (classical thermodynamics)

Constant coefficients

Order (ring theory)

Best insight from top research papers

The Makarov potential is utilized in solving the Schrodinger equation due to its ability to provide exact solutions and normalized eigenfunctions, as seen in the study by Eshghi . The Makarov potential allows for the derivation of energy eigenvalues equations using ideas from SUSY and shape invariance, enabling the study of special cases and production of valence energy states through parameter transformations. Additionally, the non-central Makarov potential discussed by Safari leads to quantum-solvable models with infinite-fold degeneracy, providing a rich framework for exploring various quantum phenomena. Overall, the Makarov potential serves as a valuable tool in quantum mechanics, offering insights into complex systems and facilitating the study of bound states and energy spectra in different physical scenarios.

Answers from top 4 papers

PDF

Open Access

More filters

Papers (4)	Insight
Journal Article•DOI A Schrödinger Potential Conditionally Integrable in Terms of the Hermite Functions T. A. Ishkhanyan, T. A. Ishkhanyan, Artur Ishkhanyan - Show less +2 more 01 Nov 2018-Physics of Atomic Nuclei 1 Citations	The Makarov potential is utilized in solving the Schrödinger equation due to its conditionally integrable nature, supporting bound states and enabling accurate energy level approximations using Hermite functions.
Open access•Posted Content Potential in the Schrodinger equation: estimation from empirical data J. L. Subias 17 Mar 2020-arXiv: General Finance 1 Citations	The Makarov potential is used in solving the Schrodinger equation to estimate classical potentials for modeling future price distributions in the stock market, as discussed in the paper.
Journal Article•DOI The solution of the Schrödinger equation for Makarov potential and homogeneous manifold $$SL (2, {\mathbb {C}})/GL (1, {\mathbb {C}})$$ S L ( 2 , C ) / G L ( 1 , C ) Farzaneh Safari 01 Dec 2020-Pramana 6 Citations	The Makarov potential is utilized to solve the Schrödinger equation due to its ability to provide energy spectrum and eigenfunctions, leading to quantum-solvable models with infinite-fold degeneracy on specific manifolds.
Open access•Journal Article•DOI Approximate solutions of Schrodinger equation and thermodynamic properties with Hua potential I. J. Njoku, C. P. Onyenegecha, C. J. Okereke, A. I. Opara, U. M. Ukewuihe, F. U. Nwaneho - Show less +5 more 01 May 2021-Results in physics 8 Citations	Not addressed in the paper.

My columns

Related Questions

What are the advantges of a differential equation approach in solving the solution for scrodinger equation for makarov potential?5 answersThe advantages of using a differential equation approach in solving the Schrodinger equation for the Makarov potential are that it allows for the development of well-posedness, existence, uniqueness, and smooth dependence with respect to the data. Additionally, this approach provides a self-contained and elementary method in an $L^{\infty}$ setting. It avoids the need for numerous and laborious coordinate transformations and series expansions, making it a simpler alternative to other known methods of solving. The Nikiforov-Uvarov method, based on solving hypergeometric type second-order differential equations using special orthogonal functions, is used to obtain exact solutions for the energy eigenvalues and eigenfunctions. The Laplace transform approach, combined with the ideas of SUSY and shape invariance, is also employed to obtain energy eigenvalues and wave functions for the angle part.

What is the projective solution of Schroedinger Equation?4 answersThe projective solution of the Schroedinger Equation is a method used to solve nonlinear evolution equations. It is a classic and efficient approach that allows for the derivation of many different solutions. The projective approach involves using ansatzs and variable separation techniques to obtain solutions for the equation. This method has been successfully applied to various systems, including the nonautonomous nonlinear Schrodinger (NLS) systemand the (2+1)-dimensional Generalized Calogero-Bogoyavlenskii-Schiff system (GCBS). The projective approach has been shown to be consistent with the compatibility condition via the Painleve analysis.

What is the role of the Coulomb potential in interactions involving charged particles?5 answersThe Coulomb potential plays a significant role in interactions involving charged particles. It affects various aspects of these interactions, including the calculation of phase shifts and wavefunctions in nuclear physics. In the study of nuclear collisions, the Coulomb interaction influences the proton and neutron density distributions, as well as the asymmetry of the systems. Additionally, in the context of Au+Au collisions, the Coulomb field generated by incident protons affects the transverse-mass and rapidity spectra of charged pions, as well as pion-pion momentum correlations. Furthermore, the Coulomb interaction can be utilized to compress a relativistic electron beam without introducing additional timing jitter, leading to enhanced temporal resolution in electron-beam-based ultrafast instruments. Overall, the Coulomb potential is a crucial factor in understanding and manipulating interactions involving charged particles.

What is schrodinger?4 answersErwin Schrödinger was a prominent physicist who made significant contributions to wave mechanics and quantum physics. He is best known for his book "What is Life?" which explored the connection between physics and biology and inspired future research on the nature of life and the genetic code. Schrödinger introduced the concept of "negative entropy" and proposed that the genetic material had a non-repetitive molecular structure, paving the way for the discovery of the secret life code. His work reshaped our understanding of life and laid the foundation for a transdisciplinary approach to studying the essence of life.

What is nonlinear scrhodinger equation?4 answersThe nonlinear Schrödinger equation is a mathematical model used to describe the behavior of waves in various physical systems. It was originally derived in the field of nonlinear optics to study the propagation of beams of light. The equation is typically written in Cartesian coordinates, but it can also be expressed in cylindrical coordinates. In this case, an additional potential term needs to be included, leading to a Gross-Pitaevskii equation instead. This modification affects the dynamics and collapse of the beam. The equation has also been applied to describe the irrotational flow of a spherical liquid layer and the behavior of nuclear clusters in deformed heavy nuclei. Additionally, q-calculus has been used to numerically solve the nonlinear Schrödinger equation, providing efficient solutions for partial differential equations. The equation is fundamental in quantum mechanics and describes the evolution of the wave function of a physical system over time. It has also been used to study the polarization mode in optical fibers, considering various physical effects.

Who create schrodinger equation?3 answersThe Schrodinger equation was created by Erwin Schrodinger in 1926. He developed this equation as a differential equation to describe the behavior of quantum mechanical particles. The equation is a fundamental component of quantum mechanics and is used to determine the wave functions of particles and how they change over time. It is worth noting that Werner Heisenberg also founded quantum mechanics in 1925 using a matrix equation, which was later found to be mathematically equivalent to Schrodinger's equation. However, there are some criticisms regarding the application of the Schrodinger equation to physical systems, as it may violate the law of conservation of energy. Despite this, Schrodinger's equation remains a crucial tool in understanding quantum mechanics and has led to significant advancements in the field.

See what other people are reading

Difference between exchange spring interaction and exchange coupling interaction in MH loops from VSM?

The key difference between exchange spring interaction and exchange coupling interaction in MH loops from VSM lies in their impact on magnetization reversal processes. Exchange spring magnets, as observed in MnGa/FeCo and CoFe2O4/FeCo bilayers, exhibit a unique behavior where the critical thickness of the soft phase is crucial for maintaining exchange coupling and enhancing energy product. On the other hand, exchange coupling interactions, such as in SmCo/FeCo core-shell nanomagnets, focus on achieving sufficient coupling effects between different magnetic phases to enhance magnetic performance. While exchange spring magnets rely on specific thicknesses for optimal performance, exchange coupling interactions aim to maximize coupling effects for improved magnetic properties. Understanding these distinctions is vital for designing advanced magnetic heterostructures with tailored magnetization behaviors.How photosynthesis proves both the law of thermodynamics?

Photosynthesis demonstrates the principles of thermodynamics through various aspects. The process of photosynthesis involves the conversion of solar energy into chemical energy, following thermodynamic laws. It can be viewed as a quantum heat engine, subject to efficiency bounds consistent with the second law of thermodynamics. Additionally, the response of photosynthesis to temperature changes can be analyzed using the generation of entropy as a criteria, showcasing the system's efficiency under different conditions. Traditional thermodynamic relationships can be applied to calculate and project photosynthesis, highlighting the energy transfer and efficiency of the process, akin to a Carnot engine cycle. Furthermore, the energy transfer mechanisms in photosynthetic systems have been scrutinized to ensure thermodynamic consistency, emphasizing the importance of adhering to thermodynamic principles in modeling energy conversion processes.What are uber strategy in bullet point using a framework?

- Uber utilized internet and social media marketing to develop its brand globally, offering customized products and services tailored to different countries and customer needs. - The company employed strategies of framing, lobbying, theorization, collaboration, and negotiation to establish legitimacy in the Brussels Capital Region, facing conflicts and special interests in the market. - Uber's success in joining the global market and positioning itself in various countries was attributed to effective business strategies and models, making it a leading company in its field. - Uber's institutional work was analyzed through the theoretical lens of institutional entrepreneurship, focusing on its actions with authorities, incumbents, drivers, and users, as well as its market strategies for legitimacy. - The analysis of Uber's strategies can be viewed through the lens of Michael Porter's generic strategies, emphasizing the importance of competitive advantage through cost, differentiation, or focus, which are critical for long-term survival and profitability.How evolution of life proves the 2nd law of thermodynamics?

The evolution of life aligns with the Second Law of Thermodynamics through the concepts of entropy and energy flow. Evolutionary entropy in replicating populations increases with scarce and diverse energy sources, mirroring thermodynamic entropy's rise in isolated systems. The emergence of life from non-living matter can be modeled as a physical phase transition, akin to thermodynamic transitions, showcasing a connection between evolution and classical thermodynamics. Life's origin and development involve complex energy transformations and organization, which can be understood through a thermodynamic lens, emphasizing the interplay between energy, entropy, and the evolution of biological systems. The compensation argument, which suggests that life's evolution does not violate the Second Law due to Earth being an open system, is critiqued for its logical shortcomings, prompting a deeper exploration of the relationship between life's emergence and thermodynamic principles.How thicker hole transport layer improves electron blocking?

Increasing the thickness of the hole transport layer can improve electron blocking by enhancing the dipole induced by the layer, leading to a gradual increase in the open-circuit voltage. This enhancement is attributed to the aggregation of molecules within the layer, which significantly boosts the dipole moment when they aggregate. Additionally, the hole transport layer's high dipole contributes to an increase in the built-in potential, compensating for non-ideal energetic alignment of charge transport levels and resulting in high open-circuit voltage. Furthermore, the insertion of a TiO2 layer as a hole-blocking layer can further improve power conversion efficiency by preventing electron leakage into the p-region, enhancing hole activation, and improving hole injection.What is freelance?

Freelance is a form of self-employment that has gained prominence due to globalization and the rise of the digital economy. The shift towards freelance work was accelerated by the 2008 international crisis, leading to organizations embracing outsourcing and independent human capital over permanent employees. Freelancing, especially in the online realm, is projected to grow significantly, with a forecasted market size increase from USD 1.6 billion in 2013 to potentially USD 46 billion by 2020. Platforms like Freelancer.com facilitate interactions between project providers and freelancers, offering a wide range of services from web design to programming. Despite challenges, entrepreneurship is increasingly seen as a viable career path for freelancers, with a focus on turning freelance activities into sustainable businesses.To what extent is the Electromagnetic spectra useful in discovering the star cycle?

The Electromagnetic spectra, particularly in the form of solar flux spectra, plays a crucial role in understanding stellar activity cycles. By comparing stellar spectra to solar flux spectra, valuable insights into stellar chemical abundances, magnetic activity phenomena, and global pulsations can be gained. Additionally, the study of neutrino-driven winds in core-collapse supernovae simulations provides further understanding of the processes influencing the synthesis of heavy elements in stars. Furthermore, observations of ultracool dwarfs suggest that these objects undergo magnetic polarity reversals akin to the Sun, challenging existing theories on magnetic field generation in fully convective stars. Therefore, the Electromagnetic spectra serves as a powerful tool in unraveling the complexities of stellar magnetic dynamos and activity cycles across a wide range of stellar types.Laziness makes more inventions?

Laziness can indeed lead to innovative solutions in various domains. In the context of secure multi-party computation, the concept of "honest but lazy" parties has driven the development of threshold multi-key fully homomorphic encryption schemes, enabling decryption with only a subset of partial decryptions, enhancing efficiency and security. Similarly, in motion planning algorithms, Lazy Shortest Path (LazySP) strategies optimize edge evaluations, showcasing asymptotically optimal performance in minimizing computational efforts. Moreover, the L4RW technique for synthesizing animations under perturbations leverages a lazy dynamic rebalance model to minimize locomotion effort, demonstrating significant speed improvements and creating more realistic animations. These instances highlight how incorporating laziness strategically can indeed foster creativity and lead to novel advancements in diverse fields.What is the repeating pattern in algebra?

Repeating patterns in algebra refer to structures where elements recur in a predictable manner. These patterns play a crucial role in developing algebraic habits of mind and advancing early algebraic concepts. They are essential for fostering relational thinking and enhancing mathematical reasoning. In the context of patterns, algebraic reasoning can be nurtured by exploring repeating patterns and their underlying structures, even without formal algebraic notation. Understanding and working with repeating patterns can serve as a bridge to developing functional thinking and laying the groundwork for more advanced algebraic concepts. While patterns are fundamental to mathematics, they are often not explicitly incorporated into formal mathematical representations, yet they play a significant role in conveying mathematical concepts and facilitating conceptual understanding.What is the L/D ration should be maintained for pressure swing adsorption?

The L/D ratio, represented by the aspect ratio L/Vbed, in pressure swing adsorption (PSA) should be smaller than 10. This ratio plays a crucial role in the efficient separation of components in a multicomponent raw material mixture. Additionally, the dimensionless cycle-compensated mass transfer coefficient, defined as KtfeedVads/Vfeed, should be maintained in the range of about 23 to 250 for optimal operation of a PSA apparatus. Furthermore, PSA processes benefit from low adsorption/desorption pressure ratios and specialized adsorbents that can selectively adsorb and release components like nitrogen at different pressure levels, enhancing the overall separation efficiency. These parameters collectively contribute to the effectiveness and performance of pressure swing adsorption systems.How can the sign of enthalpy and entropy affect gibbs free energy?

The sign of enthalpy and entropy can significantly impact Gibbs free energy. In the context of glass formation, the relationship between enthalpy and entropy is crucial, with low entropy of fusion favoring glass formation. In neurological disorders like Alzheimer's disease, a negative correlation between disease disability and Gibbs free energy was found, indicating an inverse relationship between disease entropy and thermodynamic energy. Furthermore, in the evaluation of Gibbs free energies associated with defects in crystals, it was highlighted that entropic effects play a vital role in determining free energies, emphasizing the importance of accurate free energy methods like thermodynamic integration. Therefore, the signs of enthalpy and entropy directly influence the Gibbs free energy, impacting various phenomena from glass formation to neurological conditions and crystal defects.