MORE ON PARASUPERSYMMETRIES OF THE SCHRÖDINGER EQUATION

1993 ◽  
Vol 08 (05) ◽  
pp. 435-444 ◽  
Author(s):  
J. BECKERS ◽  
N. DEBERGH ◽  
A.G. NIKITIN
Keyword(s):  
Schrödinger Equation ◽  
Differential Equations ◽  
Schrodinger Equation ◽  
Interesting Case ◽  
Second Order ◽  
Schrödinger Equations ◽  
One Dimensional ◽  
Physical Systems ◽  
Systems Of Differential Equations ◽  
General Systems

One-dimensional spatial physical systems described by Schrödinger equations with time-independent interactions admit nth order parasupersymmetries. The general systems of differential equations for the parasupersymmetric operators are obtained and superposed with previous supersymmetric results. The interesting case of second order parasupersymmetries is completely solved.

scholarly journals Solusi Analitik Persamaan Schrodinger Terdedeformasi-q dengan Potensial Kratzer dalam Sistem Koordinat Bispherical Menggunakan Metode SUSYQM

2020 ◽  
Vol 5 ◽  
Author(s):  
Dedy A Bilaut ◽  
C Cari ◽  
A Suparmi ◽  
Miftahul Ma’arif
Keyword(s):  
Analytical Solution ◽  
Schrödinger Equation ◽  
Coordinate System ◽  
Schrodinger Equation ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
One Dimensional ◽  
Eigenvalue And Eigenfunction

<p class="AbstractEnglish"><strong>Abstract:</strong> The analytical solution of the Schrodinger equation affected by Kratzer potential in Bispherical coordinate system was derived. The separable method was applied to reducing the Schrodinger equation which depends on  into three one-dimensional Schrodinger equations. The Schrodinger equations as the function of  with and without -deformed were solved using the SUSY QM method. The solutions were eigenvalue and eigenfunction of -deformed Schrodinger equation and eigenvalue end eigenfunction of Schrodinger equation with and without q-deformed in Bispherical coordinate system. The energy of the Schrodinger equation with -deformed equals to the Energy of Schrodinger without -deformed since the  parameter becomes to zero.</p><p class="AbstrakIndonesia"><strong>Abstrak:</strong> Solusi analitik dari Persamaan Schrodinger yang dipengaruhi Potensial Kratzer dalam koordinat Bispherical telah berhasil diturunkan. Metode pemisahan variabel digunakan untuk mereduksi persamaan Schrodinger yang bergantung pada  menjadi tiga persamaan Schrodinger satu dimensi. Persamaan Schrodinger fungsi  terdeformasi- dan tidak terdeformasi- diselesaikan menggunakan metode SUSY QM. Solusi yang berhasil didapatkan adalah nilai eigen dan fungsi eigen persamaan Schrodinger, masing-masing untuk sistem terdeformasi- dan yang tidak terdeformasi- dalam koordinat Bispherical. Energi dari persamaan Schrodinger terdeformasi- sama dengan energi dari persamaan Schrodinger yang tidak terdeformasi- ketika  sama dengan nol.</p>

Quantum Boxes, Stringed Instruments

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Energy Level ◽  
Schrödinger Equation ◽  
Quantum System ◽  
Schrodinger Equation ◽  
Probability Distributions ◽  
Wave Functions ◽  
Energy Level Diagram ◽  
One Dimensional ◽  
Stringed Instruments ◽  
Symmetry Properties

Chapter 7 illustrates the results obtained by applying the Schrödinger equation to a simple pedagogical quantum system, the particle in a one-dimensional box. The wave functions are seen to be sine waves; their wavelengths are evaluated and used to calculate the quantized energies via the de Broglie relation. An energy-level diagram of some of the energies is constructed; on it are illustrations of the corresponding wave functions and probability distributions. The wave functions are seen to be either symmetric or antisymmetric about the midpoint of the line representing the box, thereby providing a lead-in to the later exploration of certain symmetry properties of multi-electron atoms. It is next pointed out that the Schrödinger equation for this system is identical to Newton’s equation describing the vibrations of a stretched musical string. The different meaning of the two solutions is discussed, as is the concept and structure of linear superpositions of them.

scholarly journals Accurate Spectral Collocation Computations of High Order Eigenvalues for Singular Schrödinger Equations-Revisited

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 761
Author(s):  
Călin-Ioan Gheorghiu
Keyword(s):  
Schrödinger Equation ◽  
Small Parameter ◽  
Error Estimation ◽  
Schrodinger Equation ◽  
Error Control ◽  
High Order ◽  
Order Of Approximation ◽  
Schrödinger Equations ◽  
Spectral Collocation ◽  
Integration Interval

In this paper, we continue to solve as accurately as possible singular eigenvalues problems attached to the Schrödinger equation. We use the conventional ChC and SiC as well as Chebfun. In order to quantify the accuracy of our outcomes, we use the drift with respect to some parameters, i.e., the order of approximation N, the length of integration interval X, or a small parameter ε, of a set of eigenvalues of interest. The deficiency of orthogonality of eigenvectors, which approximate eigenfunctions, is also an indication of the accuracy of the computations. The drift of eigenvalues provides an error estimation and, from that, one can achieve an error control. In both situations, conventional spectral collocation or Chebfun, the computing codes are simple and very efficient. An example for each such code is displayed so that it can be used. An extension to a 2D problem is also considered.

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