Exact solution of the Schrodinger equation across an arbitrary one‐dimensional piecewise‐linear potential barrier

1986 ◽  
Vol 60 (5) ◽  
pp. 1555-1559 ◽  
Author(s):  
Wayne W. Lui ◽  
Masao Fukuma
Keyword(s):  
Exact Solution ◽  
Schrödinger Equation ◽  
Potential Barrier ◽  
Schrodinger Equation ◽  
Piecewise Linear ◽  
Linear Potential ◽  
One Dimensional

scholarly journals Perturbation of One-Dimensional Time Independent Schrödinger Equation With a Symmetric Parabolic Potential Wall

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1089 ◽  
Author(s):  
Soon-Mo Jung ◽  
Byungbae Kim
Keyword(s):  
Schrödinger Equation ◽  
Potential Barrier ◽  
Schrodinger Equation ◽  
Ulam Stability ◽  
One Dimensional ◽  
Parabolic Potential ◽  
Wall Potential ◽  
Finite Height ◽  
The One

The first author has recently investigated a type of Hyers-Ulam stability of the one-dimensional time independent Schrödinger equation when the relevant system has a rectangular potential barrier of finite height. In the present paper, we will investigate a type of Hyers-Ulam stability of the Schrödinger equation with the symmetric parabolic wall potential.

scholarly journals COMPLEXIFIER VERSUS FACTORIZATION AND DEFORMATION METHODS FOR GENERATION OF COHERENT STATES OF A 1D NLHO I: MATHEMATICAL CONSTRUCTION

2013 ◽  
Vol 10 (10) ◽  
pp. 1350056 ◽  
Author(s):  
R. ROKNIZADEH ◽  
H. HEYDARI
Keyword(s):  
Exact Solution ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Coherent States ◽  
Schrodinger Equation ◽  
Jacobi Polynomials ◽  
One Dimensional ◽  
The Difference ◽  
Mathematical Construction

Three methods: complexifier, factorization and deformation, for construction of coherent states are presented for one-dimensional nonlinear harmonic oscillator (1D NLHO). Since by exploring the Jacobi polynomials [Formula: see text], bridging the difference between them is possible, we give here also the exact solution of Schrödinger equation of 1D NLHO in terms of Jacobi polynomials.

scholarly journals Perturbation of the one-dimensional time-independent Schrödinger equation with a rectangular potential barrier

2020 ◽  
Vol 18 (1) ◽  
pp. 1413-1422
Author(s):  
Soon-Mo Jung ◽  
Ginkyu Choi
Keyword(s):  
Schrödinger Equation ◽  
Potential Barrier ◽  
Schrodinger Equation ◽  
Applied Mathematics ◽  
Finite Depth ◽  
Ulam Stability ◽  
Potential Well ◽  
One Dimensional ◽  
The One ◽  
Continuous Work

Abstract In Applied Mathematics Letters 74 (2017), 147–153, the Hyers-Ulam stability of the one-dimensional time-independent Schrödinger equation was investigated when the relevant system has a potential well of finite depth. As a continuous work, we prove in this paper a type of Hyers-Ulam stability of the one-dimensional time-independent Schrödinger equation with a rectangular potential barrier of {V}_{0} in height and 2c in width, where {V}_{0} is assumed to be greater than the energy E of the particle under consideration.

scholarly journals Schrödinger equation of a particle in a uniformly accelerated frame and the possibility of a new kind of quanta

2015 ◽  
Vol 30 (38) ◽  
pp. 1550182 ◽  
Author(s):  
Sanchari De ◽  
Sutapa Ghosh ◽  
Somenath Chakrabarty
Keyword(s):  
Exact Solution ◽  
Hydrogen Atom ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Minkowski Spacetime ◽  
Quantum Harmonic Oscillator ◽  
One Dimensional ◽  
Spacetime Geometry

In this paper, we have developed a formalism to obtain the Schrödinger equation for a particle in a frame undergoing a uniform acceleration in an otherwise flat Minkowski spacetime geometry. We have presented an exact solution of the equation and obtained the eigenfunctions and the corresponding eigenvalues. It has been observed that the Schrödinger equation can be reduced to a one-dimensional hydrogen atom problem. Whereas, the quantized energy levels are exactly identical with that of a one-dimensional quantum harmonic oscillator. Hence, considering transitions, we have predicted the existence of a new kind of quanta, which will either be emitted or absorbed if the particles get excited or de-excited, respectively.

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