Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

2018 ◽  
Vol 2 (2) ◽  
pp. 43-47
Author(s):  
A. Suparmi, C. Cari, Ina Nurhidayati
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Energy Spectra ◽  
Atomic Particle ◽  
Approximate Analytical Solutions ◽  
Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The  Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

REMARKS ON SUPERSYMMETRIC QUANTUM MECHANICS AND THE RADIAL SCHRÖDINGER EQUATION

1990 ◽  
Vol 05 (01) ◽  
pp. 67-70 ◽  
Author(s):  
P.K. ROY
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Supersymmetric Quantum Mechanics ◽  
Radial Schrödinger Equation

In this letter we explore two different supersymmetric connections in the radial Schrödinger equation.

The Schrödinger Equation, Path Integration and Applications

2021 ◽  
Vol 15 (01) ◽  
pp. 61-75
Author(s):  
Everaldo M. Bonotto ◽  
Felipe Federson ◽  
Márcia Federson
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Path Integration ◽  
Schrodinger Equation ◽  
Feynman Integral ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Henstock Integral ◽  
The Mean

The Schrödinger equation is fundamental in quantum mechanics as it makes it possible to determine the wave function from energies and to use this function in the mean calculation of variables, for example, as the most likely position of a group of one or more massive particles. In this paper, we present a survey on some theories involving the Schrödinger equation and the Feynman path integral. We also consider a Feynman–Kac-type formula, as introduced by Patrick Muldowney, with the Henstock integral in the description of the expectation of random walks of a particle. It is well known that the non-absolute integral defined by R. Henstock “fixes” the defects of the Feynman integral. Possible applications where the potential in the Schrödinger equation can be highly oscillating, discontinuous or delayed are mentioned in the end of the paper.

A new determination of the parameters of the optimized Heine–Abarenkov potential for 27 elements

1976 ◽  
Vol 54 (23) ◽  
pp. 2348-2354 ◽  
Author(s):  
E. R. Cowley
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Inhomogeneity Correction ◽  
Radial Schrödinger Equation

We have calculated the energy levels of the truncated Coulomb potential using numerical integration of the radial Schrödinger equation, rather than interpolation in tables. The results are used to give the parameters of the optimized Heine–Abarenkov potential for 27 elements. Various methods of weighting other contributions to the potential in the solid are used, and the inhomogeneity correction introduced by Ballentine and Gupta is discussed.

scholarly journals Non-Markovian wave-function collapse models are Bohmian-like theories in disguise

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 594
Author(s):  
Antoine Tilloy ◽  
Howard M. Wiseman
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Initial Conditions ◽  
Hidden Variables ◽  
Bohmian Mechanics ◽  
Primitive Ontology ◽  
Collapse Model ◽  
Collapse Models

Spontaneous collapse models and Bohmian mechanics are two different solutions to the measurement problem plaguing orthodox quantum mechanics. They have, a priori nothing in common. At a formal level, collapse models add a non-linear noise term to the Schrödinger equation, and extract definite measurement outcomes either from the wave function (e.g. mass density ontology) or the noise itself (flash ontology). Bohmian mechanics keeps the Schrödinger equation intact but uses the wave function to guide particles (or fields), which comprise the primitive ontology. Collapse models modify the predictions of orthodox quantum mechanics, whilst Bohmian mechanics can be argued to reproduce them. However, it turns out that collapse models and their primitive ontology can be exactly recast as Bohmian theories. More precisely, considering (i) a system described by a non-Markovian collapse model, and (ii) an extended system where a carefully tailored bath is added and described by Bohmian mechanics, the stochastic wave-function of the collapse model is exactly the wave-function of the original system conditioned on the Bohmian hidden variables of the bath. Further, the noise driving the collapse model is a linear functional of the Bohmian variables. The randomness that seems progressively revealed in the collapse models lies entirely in the initial conditions in the Bohmian-like theory. Our construction of the appropriate bath is not trivial and exploits an old result from the theory of open quantum systems. This reformulation of collapse models as Bohmian theories brings to the fore the question of whether there exists `unromantic' realist interpretations of quantum theory that cannot ultimately be rewritten this way, with some guiding law. It also points to important foundational differences between `true' (Markovian) collapse models and non-Markovian models.

scholarly journals Bound states of the D-dimensional Schrödinger equation for the generalized Woods–Saxon potential

2019 ◽  
Vol 34 (14) ◽  
pp. 1950107 ◽  
Author(s):  
V. H. Badalov ◽  
B. Baris ◽  
K. Uzun
Keyword(s):  
Quantum Mechanics ◽  
Energy Spectrum ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Basis Set ◽  
Saxon Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Approximate Analytical Solutions

The formal framework for quantum mechanics is an infinite number of dimensional space. Hereby, in any analytical calculation of the quantum system, the energy eigenvalues and corresponding wave functions can be represented easily in a finite-dimensional basis set. In this work, the approximate analytical solutions of the hyper-radial Schrödinger equation are obtained for the generalized Wood–Saxon potential by implementing the Pekeris approximation to surmount the centrifugal term. The energy eigenvalues and corresponding hyper-radial wave functions are derived for any angular momentum case by means of state-of-the-art Nikiforov–Uvarov and supersymmetric quantum mechanics methods. Hence, the same expressions are obtained for the energy eigenvalues, and the expression of hyper-radial wave functions transforming each other is shown owing to these methods. Furthermore, a finite number energy spectrum depending on the depths of the potential well [Formula: see text] and [Formula: see text], the radial [Formula: see text] and [Formula: see text] orbital quantum numbers and parameters [Formula: see text], [Formula: see text], [Formula: see text] are also identified in detail. Next, the bound state energies and corresponding normalized hyper-radial wave functions for the neutron system of the [Formula: see text]Fe nucleus are calculated in [Formula: see text] and [Formula: see text] as well as the energy spectrum expressions of other higher dimensions are revealed by using the energy spectrum of [Formula: see text] and [Formula: see text].

scholarly journals A Refined Propensity Account for GRW Theory

2021 ◽  
Vol 51 (2) ◽  
Author(s):  
Lorenzo Lorenzetti
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Precise Nature ◽  
Dispositional Account ◽  
Collapse Theories ◽  
Dispositional Properties

AbstractSpontaneous collapse theories of quantum mechanics turn the usual Schrödinger equation into a stochastic dynamical law. In particular, in this paper I will focus on the GRW theory. Two philosophical issues that can be raised about GRW concern (a) the ontology of the theory, in particular the nature of the wave function and its role within the theory, and (b) the interpretation of the objective probabilities involved in the dynamics of the theory. During the last years, it has been claimed that we can take advantage of dispositional properties in order to develop an ontology for GRW theory, and also in order to ground the objective probabilities which are postulated by it. However, in this paper I will argue that the dispositional interpretations which have been discussed in the literature so far are either flawed or—at best—incomplete. If we want to endorse a dispositional interpretation of GRW theory we thus need an extended account which specifies the precise nature of those properties and which makes also clear how they can correctly ground all the probabilities postulated by the theory. Thus, after having introduced several different kinds of probabilistic dispositions, I will try to fill the gap in the literature by proposing a novel and complete dispositional account of GRW, based on what I call spontaneous weighted multi-track propensities. I claim that such an account can satisfy both of our desiderata.

scholarly journals Schrodinger Equation in Cosmological Inertial Frame

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Wave Equation ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Inertial Frame ◽  
Special Theory ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Klein Gordon

Schrodinger equation is a wave equation. Wave function uses as a probability amplitude in quantum mechanics. We make Schrodinger equation from Klein-Gordon free particle’s wave function in cosmological special theory of relativity.

SCATTERING STATES OF HULTHÉN INTERACTION IN MINIMAL LENGTH QUANTUM MECHANICS

2013 ◽  
Vol 28 (12) ◽  
pp. 1350041 ◽  
Author(s):  
H. HASSANABADI ◽  
S. ZARRINKAMAR ◽  
E. MAGHSOODI
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Effective Potential ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Reflection Coefficients ◽  
Transmission And Reflection Coefficients ◽  
Scattering States ◽  
Vector Interaction ◽  
Transmission And Reflection

We first revisit the nonrelativistic minimal length quantum mechanics and reveal an interesting symmetry of the problem. In fact, we will show that the cumbersome problem can be cast into the ordinary Schrödinger equation with a new effective potential. Next, as a typical example, we show the minimal length Schrödinger equation in the presence of a nonminimal Hulthén vector interaction. The transmission and reflection coefficients are reported as well.

Time Evolution of Some Modified Nonrelativistic Hamiltonians

2015 ◽  
Vol 70 (1) ◽  
pp. 69-72
Author(s):  
Hassan Hassanabadi ◽  
Parisa Hooshmand
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Time Evolution ◽  
Schrodinger Equation ◽  
Free Particle ◽  
Minimal Length ◽  
Basic Concepts

AbstractThe modified Schrödinger equation due to its minimal length is considered useful for harmonic and linear potentials, as well as the free-particle case. Using basic concepts of quantum mechanics, the time evolution of these systems is reported.

Sign in / Sign up

Export Citation Format

Share Document