Semiclassical matrix mechanics. I. The harmonic oscillator

1990 ◽  
Vol 51 (1) ◽  
pp. 47-58 ◽  
Author(s):  
R.M. More
Keyword(s):  
Harmonic Oscillator ◽  
Matrix Mechanics

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.

Rosen-Chambers Variation Theory of Linearly-Damped Classic and Quantum Oscillator

2014 ◽  
Vol 4 (1) ◽  
pp. 404-426
Author(s):  
Vincze Gy. Szasz A.
Keyword(s):  
Harmonic Oscillator ◽  
Classical Mechanics ◽  
Universal Time ◽  
Variation Theory ◽  
Quantum Oscillator ◽  
Variation Principle ◽  
Poisson Brackets ◽  
Mathematical Meaning ◽  
Damped Harmonic Oscillator ◽  
Damped Oscillator

Phenomena of damped harmonic oscillator is important in the description of the elementary dissipative processes of linear responses in our physical world. Its classical description is clear and understood, however it is not so in the quantum physics, where it also has a basic role. Starting from the Rosen-Chambers restricted variation principle a Hamilton like variation approach to the damped harmonic oscillator will be given. The usual formalisms of classical mechanics, as Lagrangian, Hamiltonian, Poisson brackets, will be covered too. We shall introduce two Poisson brackets. The first one has only mathematical meaning and for the second, the so-called constitutive Poisson brackets, a physical interpretation will be presented. We shall show that only the fundamental constitutive Poisson brackets are not invariant throughout the motion of the damped oscillator, but these show a kind of universal time dependence in the universal time scale of the damped oscillator. The quantum mechanical Poisson brackets and commutation relations belonging to these fundamental time dependent classical brackets will be described. Our objective in this work is giving clearer view to the challenge of the dissipative quantum oscillator.

On the relativistic harmonic oscillator equations for the unequal masses quark-antiquark system

1980 ◽  
Vol 66 (1) ◽  
pp. 865-872
Author(s):  
Jacques Bijtebier ◽  
F. Dubois
Keyword(s):  
Harmonic Oscillator ◽  
Relativistic Harmonic Oscillator ◽  
Oscillator Equations

scholarly journals Two-dimensional isotropic harmonic oscillator on a time-dependent sphere

2012 ◽  
Vol 45 (46) ◽  
pp. 465301 ◽  
Author(s):  
Ali Mahdifar ◽  
Behrouz Mirza ◽  
Rasoul Roknizadeh
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Two Dimensional ◽  
Isotropic Harmonic Oscillator
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