scholarly journals A geodesical approach for the harmonic oscillator

2020 ◽  
Vol 17 (1 Jan-Jun) ◽  
pp. 6
Author(s):  
Rodrigo Sánchez-Martínez ◽  
Alvaro Lorenzo Salas-Brito ◽  
Hilda Noemí Núñez-Yépez
Keyword(s):  
Harmonic Oscillator ◽  
Kepler Problem ◽  
Spherical Surface ◽  
Free Particle ◽  
Theoretical Physics ◽  
Canonical Transformations ◽  
Canonical Coordinates ◽  
One Dimensional ◽  
Particle Form ◽  
The One

The harmonic oscillator (HO) is present in all contemporary physics, from elementary classical mechanicsto quantum field theory. It is useful in general to exemplify techniques in theoretical physics. In this work,we use a method for solving classical mechanic problems by first transforming them to a free particle formand using the new canonical coordinates to reparametrize its phase space. This technique has been used tosolve the one-dimensional hydrogen atom and also to solve for the motion of a particle in a dipolar potential.Using canonical transformations we convert the HO Hamiltonian to a free particle form which becomestrivial to solve. Our approach may be helpful to exemplify how canonical transformations may be used inmechanics. Besides, we expect it will help students to grasp what they mean when it is said that a problemhas been transformed into another completely different one. As, for example, when the Kepler problem istransformed into free (geodesic) motion on a spherical surface.

One-Dimensional Harmonic Oscillator in Quantum Phase Space

2011 ◽  
Vol 110-116 ◽  
pp. 3750-3754
Author(s):  
Jun Lu ◽  
Xue Mei Wang ◽  
Ping Wu
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Quantum Phase ◽  
Space Representation ◽  
Wave Mechanics ◽  
One Dimensional ◽  
Matrix Mechanics ◽  
The Matrix ◽  
Quantum Wave ◽  
The One

Within the framework of the quantum phase space representation established by Torres-Vega and Frederick, we solve the rigorous solutions of the stationary Schrödinger equations for the one-dimensional harmonic oscillator by means of the quantum wave-mechanics method. The result shows that the wave mechanics and the matrix mechanics are equivalent in phase space, just as in position or momentum space.

THE ONE-DIMENSIONAL HARMONIC OSCILLATOR

1978 ◽  
pp. 60-75
Author(s):  
JOHN P. LOWE
Keyword(s):  
Harmonic Oscillator ◽  
One Dimensional ◽  
The One

THE ONE-DIMENSIONAL HARMONIC OSCILLATOR

1993 ◽  
pp. 67-85
Author(s):  
John P. Lowe
Keyword(s):  
Harmonic Oscillator ◽  
One Dimensional ◽  
The One

Quantum mechanics on (anti)-de Sitter background II: Ramsauer–Townsend effect and WKB method

2018 ◽  
Vol 33 (26) ◽  
pp. 1850150 ◽  
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Quantum Mechanics ◽  
Energy Level ◽  
Harmonic Oscillator ◽  
Wkb Method ◽  
De Sitter ◽  
Quantum Harmonic Oscillator ◽  
One Dimensional ◽  
Sitter Background ◽  
The One

Based on the one-dimensional quantum mechanics on (anti)-de Sitter background [W. S. Chung and H. Hassanabadi, Mod. Phys. Lett. A 32, 26 (2107)], we discuss the Ramsauer–Townsend effect. We also formulate the WKB method for the quantum mechanics on (anti)-de Sitter background to discuss the energy level of the quantum harmonic oscillator and quantum bouncer.

su (2) Lie algebra approach for the Feynman propagator of the one-dimensional harmonic oscillator

2014 ◽  
Vol 35 (3) ◽  
pp. 035001
Author(s):  
D Martínez ◽  
C G Avendaño
Keyword(s):  
Harmonic Oscillator ◽  
Lie Algebra ◽  
Feynman Propagator ◽  
One Dimensional ◽  
Algebra Approach ◽  
The One

ON A PROBLEM OF GEOMETRIC QUANTIZATION

2011 ◽  
Vol 08 (06) ◽  
pp. 1259-1268 ◽  
Author(s):  
CIPRIAN HEDREA ◽  
ROMEO NEGREA ◽  
IOAN ZAHARIE ◽  
MIRCEA PUTA
Keyword(s):  
Harmonic Oscillator ◽  
Geometric Quantization ◽  
One Dimensional ◽  
The One

The problem of geometric Kostant quantization of this paper is the role played by "½-correction forms" in order to arrive at the result given by the classical Schrödinger quantization, in the one-dimensional harmonic oscillator study.

Quantum mechanics of the damped harmonic oscillator

2002 ◽  
Vol 80 (6) ◽  
pp. 645-660 ◽  
Author(s):  
M Blasone ◽  
P Jizba
Keyword(s):  
Harmonic Oscillator ◽  
Ground State ◽  
Geometric Phase ◽  
State Energy ◽  
Dimensional System ◽  
One Dimensional ◽  
Damped Harmonic Oscillator ◽  
Linear Harmonic Oscillator ◽  
Two Dimensional System ◽  
The One

We quantize the system of a damped harmonic oscillator coupled to its time-reversed image, known as Bateman's dual system. By using the Feynman–Hibbs method, the time-dependent quantum states of such a system are constructed entirely in the framework of the classical theory. The geometric phase is calculated and found to be proportional to the ground-state energy of the one-dimensional linear harmonic oscillator to which the two-dimensional system reduces under appropriate constraint. PACS Nos.: 03.65Ta, 03.65Vf, 03.65Ca, 03.65Fd

scholarly journals Non-Standard and Numerov Finite Difference Schemes for Finite Difference Time Domain Method to Solve One- Dimensional Schrödinger Equation

2018 ◽  
Vol 2 (1) ◽  
pp. 27
Author(s):  
Lily Maysari Angraini ◽  
I Wayan Sudiarta
Keyword(s):  
Finite Difference ◽  
Harmonic Oscillator ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Fdtd Method ◽  
Finite Difference Schemes ◽  
Potential Wells ◽  
One Dimensional ◽  
The One ◽  
Difference Time

<span>The purpose of  this paper is to show some improvements of the finite-difference time domain (FDTD) method using Numerov and non-standard finite difference (NSFD) schemes for solving the one-dimensional Schr</span><span>ö</span><span>dinger equation. Starting with results of the unmodified FDTD method, Numerov-FD and NSFD are applied iteratively to produce more accurate results for eigen energies and wavefunctios. Three potential wells, infinite square well, harmonic oscillator and Poschl-Teller, are used to compare results of FDTD calculations. Significant improvements in the results for the infinite square potential and the harmonic oscillator potential are found using Numerov-NSFD scheme, and for Poschl-Teller potential are found using Numerov scheme.</span>

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