scholarly journals Curvature-dependent formalism, Schrödinger equation and energy levels for the harmonic oscillator on three-dimensional spherical and hyperbolic spaces

2012 ◽  
Vol 45 (26) ◽  
pp. 265303 ◽  
Author(s):  
José F Cariñena ◽  
Manuel F Rañada ◽  
Mariano Santander
Keyword(s):  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Three Dimensional ◽  
Hyperbolic Spaces

scholarly journals THE q-DEFORMED SCHRÖDINGER EQUATION OF THE HARMONIC OSCILLATOR ON THE QUANTUM EUCLIDEAN SPACE

1994 ◽  
Vol 09 (22) ◽  
pp. 3989-4008 ◽  
Author(s):  
URSULA CAROW-WATAMURA ◽  
SATOSHI WATAMURA
Keyword(s):  
Euclidean Space ◽  
Difference Equation ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Series Representation ◽  
Exponential Functions ◽  
Creation And Annihilation Operators ◽  
The Creation

We consider the q-deformed Schrödinger equation of the harmonic oscillator on the N-dimensional quantum Euclidean space. The creation and annihilation operators are found, which systematically produce all energy levels and eigenfunctions of the Schrödinger equation. In order to get the q series representation of the eigenfunction, we also give an alternative way to solve the Schrödinger equation which is based on the q analysis. We represent the Schrödinger equation by the q difference equation and solve it by using q polynomials and q exponential functions.

scholarly journals Approximate Solution of Schrödinger Equation with Pseudo-Gaussian Potential Viewed as a Perturbation

2015 ◽  
Vol 58 (1) ◽  
pp. 7-13
Author(s):  
Theodor-Felix Iacob ◽  
Marina Lute ◽  
Felix Iacob
Keyword(s):  
Approximate Solution ◽  
Power Series ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Additional Term ◽  
Oscillator Potential ◽  
Harmonic Oscillator Potential ◽  
Gaussian Potential

Abstract We consider the Schrödinger equation with pseudo-Gaussian potential and point out that it is basically made up by a term representing the harmonic oscillator potential and an additional term, which is actually a power series that converges rapidly. Based on this observation the system can be considered as a perturbation of harmonic oscillator. The perturbation method is used to approximate the energy levels of pseudo- Gaussian oscillator. The results are compared with those obtained in the analytic and numeric case.

Quasi-bound state calculations for several types of potential in one-, two-, and three-dimensional systems, using perturbative techniques

1993 ◽  
Vol 71 (3-4) ◽  
pp. 133-141 ◽  
Author(s):  
M. R. M. Witwit
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Dimensional Space ◽  
Energy Levels ◽  
Three Dimensional ◽  
Bound State ◽  
Inner Product ◽  
Model Potentials ◽  
Three Dimensional Space ◽  
Quasi Bound State

The energy levels of the Schrödinger equation for various model potentials in one-, two-, and three-dimensional space are calculated using the hypervirial and inner product methods.

scholarly journals The noncommutative Coulomb potential

2021 ◽  
pp. 2150094
Author(s):  
B. C. Wang ◽  
E. C. Brenag ◽  
R. G. G. Amorim ◽  
V. C. Rispoli ◽  
S. C. Ulhoa
Keyword(s):  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Potential Problem ◽  
Energy Levels ◽  
Three Dimensional

In this work, we analyze the noncommutative three-dimensional Coulomb potential problem. For this purpose, we used the Kustaanheimo–Stiefel mapping to write the Schrödinger equation for Coulomb potential in a solvable way. Then, the noncommutative hydrogen-like atoms were treated, and their energy levels were found. In addition, we estimate a bound for the noncommutativity parameter.

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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