Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
On the quantization of linearly damped harmonic oscillator
View through CrossRef
Using the equation of motion for a linearly damped harmonic oscillator as fundamental equation, a condition has been obtained that must be satisfied by its Lagrangian and a number of functional forms has been critically investigated. The Lagrangians that successfully describe a classical damped oscillator have been quantized using Feynman’s elegant path integral method. However, it is found that the expectation value of energy of the damped oscillator in all the cases becomes infinitely large for t→∞, ruling out the possibility of treating the damped quantum system as a one-body problem.
Title: On the quantization of linearly damped harmonic oscillator
Description:
Using the equation of motion for a linearly damped harmonic oscillator as fundamental equation, a condition has been obtained that must be satisfied by its Lagrangian and a number of functional forms has been critically investigated.
The Lagrangians that successfully describe a classical damped oscillator have been quantized using Feynman’s elegant path integral method.
However, it is found that the expectation value of energy of the damped oscillator in all the cases becomes infinitely large for t→∞, ruling out the possibility of treating the damped quantum system as a one-body problem.
Related Results
Constrained Quantization for Probability Distributions
Constrained Quantization for Probability Distributions
In this work, we extend the classical framework of quantization for Borel probability measures defined on normed spaces Rk by introducing and analyzing the notions of the nth const...
Mitigating Quantization Errors Due to Activation Spikes in Gated Linear Unit-Based Large Language Models
Mitigating Quantization Errors Due to Activation Spikes in Gated Linear Unit-Based Large Language Models
Modern large language models (LLMs) achieve state-of-the-art performance through architectural advancements but require high computational costs for inference. Post-training quanti...
Theoretical investigation of injection-locked differential oscillator
Theoretical investigation of injection-locked differential oscillator
A preliminary analysis of published works on this topic showed that at present there is no sufficiently substantiated theory of such devices, and the approximate approaches used ar...
Exact Solutions for Strong Nonlinear Oscillators with Linear Damping
Exact Solutions for Strong Nonlinear Oscillators with Linear Damping
This paper presents the derivation of an exact solution for a damped nonlinear oscillator of arbitrary order (both integer and non-integer). A coefficient relationship was defined ...
Solving Undamped and Damped Fractional Oscillators via Integral Rohit Transform
Solving Undamped and Damped Fractional Oscillators via Integral Rohit Transform
Background: The dynamics of fractional oscillators are generally described by fractional differential equations, which include the fractional derivative of the Caputo or Riemann-Li...
Stability switching behavior of thermoacoustic oscillation in Rijke tube
Stability switching behavior of thermoacoustic oscillation in Rijke tube
Large-amplitude self-excited thermoacoustic oscillations arising due to the interaction between unsteady heat release and acoustic pressure fluctuations have been encountered in ma...
Modelling and analysis of LCC‐HVDC converter station for harmonic coupling of AC/DC power grid during geomagnetic storm
Modelling and analysis of LCC‐HVDC converter station for harmonic coupling of AC/DC power grid during geomagnetic storm
AbstractIn this paper, the problem of harmonic coupling between the converter transformer and the converter under the action of geomagnetically induced current (GIC) is proposed to...
COMPUTATIONAL DESCRIPTION OF THE SIMPLE HARMONIC OSCILLATOR AND THE SIMPLE PENDULUM
COMPUTATIONAL DESCRIPTION OF THE SIMPLE HARMONIC OSCILLATOR AND THE SIMPLE PENDULUM
A comparison between the equations of motion and periods of a simple pendulum and a simple harmonic oscillator was made using a computational technique. The equation of motion of t...