REVISED EQUATION OF MOTION METHOD, SEMI-CLASSICAL LIMIT, AND MATHEMATICALLY CLOSED THEORY OF LARGE AMPLITUDE COLLECTIVE MOTION

1984 ◽  
Vol 45 (C6) ◽  
pp. C6-111-C6-119
Author(s):  
A. Klein
Keyword(s):  
Large Amplitude ◽  
Classical Limit ◽  
Collective Motion ◽  
Equation Of Motion ◽  
Closed Theory ◽  
Motion Method

q-Equivalent Hamiltonian Operators

1972 ◽  
Vol 50 (17) ◽  
pp. 2037-2047 ◽  
Author(s):  
M. Razavy
Keyword(s):  
Quantum Mechanics ◽  
Classical Limit ◽  
First Integral ◽  
Canonical Commutation Relation ◽  
Equation Of Motion ◽  
First Integrals ◽  
Position Operator ◽  
Integrals Of Motion ◽  
Adjoint Operators ◽  
Hamiltonian Operators

From the equation of motion and the canonical commutation relation for the position of a particle and its conjugate momentum, different first integrals of motion can be constructed. In addition to the proper Hamiltonian, there are other operators that can be considered as the generators of motion for the position operator (q-equivalent Hamiltonians). All of these operators have the same classical limit for the probability density of the coordinate of the particle, and many of them are symmetric and self-adjoint operators or have self-adjoint extensions. However, they do not satisfy the Heisenberg rule of quantization, and lead to incorrect commutation relations for velocity and position operators. Therefore, it is concluded that the energy first integral and the potential, rather than the equation of motion and the force law, are the physically significant operators in quantum mechanics.

Large-Amplitude Collective Motion

1996 ◽  
pp. 317-358
Author(s):  
Walter Greiner ◽  
Joachim A. Maruhn
Keyword(s):  
Large Amplitude ◽  
Collective Motion

Theoretical Study on the Transport through a Quantum Dots Array with a Side Quantum Dot

2011 ◽  
Vol 340 ◽  
pp. 331-336
Author(s):  
Hai Tao Yin ◽  
Xiao Jie Liu ◽  
Wei Long Wan ◽  
Cheng Bao Yao ◽  
Li Na Bai ◽  
...  
Keyword(s):  
Quantum Dots ◽  
Green Function ◽  
Energy Level ◽  
Quantum Dot ◽  
Quantum Interference ◽  
Theoretical Study ◽  
Equation Of Motion ◽  
Function Technique ◽  
Motion Method ◽  
Linear Conductance

We studied transport properties through a noninteracting quantum dots array with a side quantum dot employing the equation of motion method and Green function technique. The linear conductance has been calculated numerically. It is shown that an antiresonance always pinned at the energy level of side quantum dot. The conductance develops Fano line shape when the side quantum dot level is not aligned with that of the quantum dots in the array due to quantum interference through different channels.

Sign in / Sign up

Export Citation Format

Share Document