Phase-Space Wave Functions of Harmonic Oscillator in Nanomaterials

2011 ◽  
Vol 233-235 ◽  
pp. 2154-2157
Author(s):  
Jun Lu
Keyword(s):  
Wave Function ◽  
Phase Space ◽  
Harmonic Oscillator ◽  
Wave Functions ◽  
Quantum Phase ◽  
Space Representation ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Phase Space Representation ◽  
Space Wave

In this paper, we solve the rigorous solutions of the stationary Schrödinger equations for the harmonic oscillator in nanomaterials within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. We obtain the phase-space eigenfunctions of the harmonic oscillator. We also discuss the character of wave function and the “Fourier-like” projection transformations in phase space.

Phase-Space Wave Functions of Diatomic System in One-Dimensional Nanomaterials

2011 ◽  
Vol 474-476 ◽  
pp. 1179-1182
Author(s):  
Jun Lu
Keyword(s):  
Phase Space ◽  
Exact Solutions ◽  
Potential Function ◽  
Wave Functions ◽  
Space Representation ◽  
One Dimensional ◽  
Empirical Potential ◽  
Diatomic System ◽  
Phase Space Representation ◽  
Space Wave

The exact solutions of the stationary Schrödinger equations for the diatomic system with an empirical potential function in one-dimensional nanomaterials are solved within the framework of the quantum phase-space representation established by Torres-Vega and Frederick. The wave functions in position and momentum representations can be obtained through the Fourier-like projection transformation from the phase-space wave functions.

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 Hulthén potential in the quantum phase space representation

Open Physics ◽  
2014 ◽  
Vol 12 (2) ◽  
Author(s):  
Jerzy Stanek
Keyword(s):  
Phase Space ◽  
Wigner Function ◽  
Quantum Phase ◽  
Space Representation ◽  
Hulthén Potential ◽  
One Dimensional ◽  
Hulthen Potential ◽  
Analytic Expression ◽  
The One ◽  
Phase Space Representation

AbstractThe analytic expression of the Wigner function for bound eigenstates of the Hulthén potential in quantum phase space is obtained and presented by plotting this function for a few quantum states. In addition, the correct marginal distributions of the Wigner function in spherical coordinates are determined analytically.

Inelastic atom-diatom scattering in quantum phase space representation

1994 ◽  
Vol 230 (3) ◽  
pp. 217-222 ◽  
Author(s):  
Xu-Guang Hu ◽  
Qian-Shu Li ◽  
Au-Chin Tang
Keyword(s):  
Phase Space ◽  
Quantum Phase ◽  
Space Representation ◽  
Phase Space Representation
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