Real wavefunction from Generalised Hamiltonian Schrodinger Equation in quantum phase space via HOA (Heaviside Operational Ansatz): exact analytical results

2014 ◽  
Vol 52 (4) ◽  
pp. 1137-1155 ◽  
Author(s):  
Valentino A. Simpao
Keyword(s):  
Phase Space ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Quantum Phase ◽  
Analytical Results

Contracted Schrödinger equation in quantum phase-space

2017 ◽  
Vol 39 (17) ◽  
pp. 1068-1075
Author(s):  
Carol Frishberg ◽  
Leon Cohen
Keyword(s):  
Phase Space ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Quantum Phase

SPATIOTEMPORAL PATTERNS IN LANGMUIR PLASMAS

1994 ◽  
Vol 08 (24) ◽  
pp. 1503-1510 ◽  
Author(s):  
CANGTAO ZHOU ◽  
X.T. HE
Keyword(s):  
Phase Space ◽  
Schrödinger Equation ◽  
Spatial Patterns ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Numerical Results ◽  
Spatiotemporal Patterns ◽  
Two Dimensional ◽  
Fourier Space ◽  
Quintic Nonlinear Schrödinger Equation

The constitutions of the phase space, stochasticity, and the complicated patterns of Langmuir fields are investigated in terms of a two-dimensional cubic-quintic nonlinear Schrödinger equation. The numerical results obviously illustrate that the quintic non-linearity leads to the production of the complicated patterns. The mechanism to form these spatial patterns is also analyzed by measuring the spectrum of energy in Fourier space. It is shown that the complicated patterns are associated with the complexity of trajectory in phase space and the stochastic partition of energy in Fourier modes.

ARBITRARY l-WAVE BOUND STATE SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH THE ECKART POTENTIAL

2009 ◽  
Vol 23 (18) ◽  
pp. 2269-2279 ◽  
Author(s):  
YONG-FENG DIAO ◽  
LIANG-ZHONG YI ◽  
TAO CHEN ◽  
CHUN-SHENG JIA
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Approximation Scheme ◽  
Function Analysis ◽  
Bound State ◽  
Centrifugal Term ◽  
Radial Wave ◽  
Shape Invariance ◽  
Eckart Potential ◽  
Analytical Results

By using a modified approximation scheme to deal with the centrifugal term, we solve approximately the Schrödinger equation for the Eckart potential with the arbitrary angular momentum states. The bound state energy eigenvalues and the unnormalized radial wave functions are approximately obtained in a closed form by using the supersymmetric shape invariance approach and the function analysis method. The numerical experiments show that our analytical results are in better agreement with those obtained by using the numerical integration approach than the analytical results obtained by using the conventional approximation scheme to deal with the centrifugal term.

Repulsive Nonlinear Schrödinger Equation and Bose-Einstein Condensate in Phase Space

2011 ◽  
Vol 403-408 ◽  
pp. 132-137
Author(s):  
Jun Lu ◽  
Yun Zhi Wang ◽  
Xiao Yun Mu
Keyword(s):  
Phase Space ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Einstein Condensate ◽  
Nonlinear Schrodinger Equation ◽  
Space Representation ◽  
Nonlinear Schrödinger ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Phase Space Representation

Within the framework of the quantum phase-space representation established by Torres-Vega and Frederick, the rigorous solutions of repulsive nonlinear Schrödinger equation are solved, which models the dilute-gas Bose-Einstein condensate. The eigenfunctions in position and momentum spaces can be obtained through the “Fourier-like” projection transformation from the phase-space eigenfunctions. It shows that the wave-mechanics method in the phase-space representation could be extended to the nonlinear Schrödinger equations. The research provides the foundation for the approximate calculation in future.

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