QUANTUM AND THERMAL STATE FOR EXPONENTIALLY DAMPED HARMONIC OSCILLATOR WITH AND WITHOUT INVERSE QUADRATIC POTENTIAL

2002 ◽  
Vol 16 (09) ◽  
pp. 1341-1351 ◽  
Author(s):  
J. R. CHOI
Keyword(s):  
Harmonic Oscillator ◽  
Density Operator ◽  
Thermal State ◽  
Mechanical Energy ◽  
Invariant Operator ◽  
Diagonal Element ◽  
Quadratic Potential ◽  
Damped Harmonic Oscillator ◽  
Energy Expectation ◽  
Quantum Mechanical Energy

By taking advantage of dynamical invariant operator, we derived Schrödinger solution for exponentially damped harmonic oscillator with and without inverse quadratic potential. We investigated quantum mechanical energy expectation value, uncertainty relation, partition function and density operator of the system. The various expectation values in thermal state are calculated using the diagonal element of density operator.

On classical and quantum harmonic potentials

2000 ◽  
Vol 78 (10) ◽  
pp. 937-946 ◽  
Author(s):  
P Mohazzabi
Keyword(s):  
Potential Energy ◽  
Harmonic Oscillator ◽  
Energy Function ◽  
Mechanical Energy ◽  
Energy Levels ◽  
Potential Energy Function ◽  
Quantum Mechanical ◽  
Quantum Mechanical Energy

To date, the only potential energy function that has been demonstrated to be classical harmonic but not quantum harmonic is that of the asymmetrically matched harmonic oscillator. By investigating the accurate quantum mechanical energy levels of the potential V = V0 [Formula: see text], we demonstrate that this is the second member of the class. PACS No.: 03.65Ge

WAVE FUNCTIONS WITH DISCRETE AND WITH CONTINUOUS SPECTRUM FOR QUANTUM DAMPED HARMONIC OSCILLATOR PERTURBED BY A SINGULARITY

2004 ◽  
Vol 18 (07) ◽  
pp. 1007-1020 ◽  
Author(s):  
JEONG-RYEOL CHOI
Keyword(s):  
Harmonic Oscillator ◽  
Continuous Spectrum ◽  
Unitary Operator ◽  
Invariant Operator ◽  
Confluent Hypergeometric Function ◽  
Quantum States ◽  
Wave Functions ◽  
The Other ◽  
Damped Harmonic Oscillator ◽  
Discrete And Continuous Spectrum

The quantum states with discrete and continuous spectrum for the damped harmonic oscillator perturbed by a singularity have been investigated using invariant operator and unitary operator together. The eigenvalue of the invariant operator for ω0≤β/2 is continuous while for ω0>β/2 is discrete. The wave functions for ω0=β/2 expressed in terms of the Bessel function and for ω0<β/2 in terms of the Kummer confluent hypergeometric function. The convergence of the probability density is more rapid for over-damped harmonic oscillator than that of the other two cases due to the large damping constant.

scholarly journals Analyzing Density Operator in Thermal State for Complicated Time-Dependent Optical Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Jeong Ryeol Choi ◽  
Ji Nny Song ◽  
Yeontaek Choi
Keyword(s):  
Optical System ◽  
Operator Theory ◽  
Density Operator ◽  
Thermal State ◽  
Invariant Operator ◽  
Quantum States ◽  
Time Dependent ◽  
Optical Systems ◽  
Time Varying ◽  
The One

Density operator of oscillatory optical systems with time-dependent parameters is analyzed. In this case, a system is described by a time-dependent Hamiltonian. Invariant operator theory is introduced in order to describe time-varying behavior of the system. Due to the time dependence of parameters, the frequency of oscillation, so-called a modified frequency of the system, is somewhat different from the natural frequency. In general, density operator of a time-dependent optical system is represented in terms of the modified frequency. We showed how to determine density operator of complicated time-dependent optical systems in thermal state. Usually, density operator description of quantum states is more general than the one described in terms of the state vector.

scholarly journals Thermalization in a Quantum Harmonic Oscillator with Random Disorder

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 855
Author(s):  
Ya-Wei Hsueh ◽  
Che-Hsiu Hsueh ◽  
Wen-Chin Wu
Keyword(s):  
Numerical Simulation ◽  
Equilibrium State ◽  
Harmonic Oscillator ◽  
Total Energy ◽  
Mechanical Energy ◽  
Nonequilibrium State ◽  
Quantum Harmonic Oscillator ◽  
Damped Harmonic Oscillator ◽  
Random Disorder ◽  
Kinetic And Potential Energies

We propose a possible scheme to study the thermalization in a quantum harmonic oscillator with random disorder. Our numerical simulation shows that through the effect of random disorder, the system can undergo a transition from an initial nonequilibrium state to a equilibrium state. Unlike the classical damped harmonic oscillator where total energy is dissipated, total energy of the disordered quantum harmonic oscillator is conserved. In particular, at equilibrium the initial mechanical energy is transformed to the thermodynamic energy in which kinetic and potential energies are evenly distributed. Shannon entropy in different bases are shown to yield consistent results during the thermalization.

COHERENT STATES OF NONCONSERVATIVE HARMONIC OSCILLATOR WITH A SINGULAR PERTURBATION

2003 ◽  
Vol 17 (12) ◽  
pp. 2429-2437 ◽  
Author(s):  
JEONG RYEOL CHOI
Keyword(s):  
Singular Perturbation ◽  
Coherent State ◽  
Harmonic Oscillator ◽  
Coherent States ◽  
Mechanical Energy ◽  
Invariant Operator ◽  
Expectation Values ◽  
Raising Operators ◽  
The Difference

We investigated the coherent states of nonconservative harmonic oscillator with a singular perturbation. The invariant operator represented in terms of lowering and raising operators. We confirmed that if the difference between two eigenvalues, α and β, of coherent states is much larger than unity, the states |α> and |β> are approximately orthogonal to each another. We calculated the expectation values of various quantities such as invariant operator, Hamiltonian and mechanical energy in coherent state. The mechanical energy of the system described by the Kanai–Caldirola Hamiltonian decreased exponentially depending on γ as time goes by in coherent state.

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.

Path integral for the damped harmonic oscillator coupled to its dual

1994 ◽  
Vol 35 (3) ◽  
pp. 1185-1191 ◽  
Author(s):  
L. Chetouani ◽  
L. Guechi ◽  
T. F. Hammann ◽  
M. Letlout
Keyword(s):  
Harmonic Oscillator ◽  
Path Integral ◽  
Damped Harmonic Oscillator
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