China
Africa
Explore chapters and articles related to this topic
Black-body Radiation, Einstein and Planck's Law
Published in Caio Lima Firme, Quantum Mechanics, 2022
A harmonic oscillator is a system that is displaced from its equilibrium position experiencing a restoring force proportional to its displacement having sinusoidal oscillations about the equilibrium point. Simple mechanics examples are pendulums and masses connected to springs. The light has two sinusoidal oscillating fields (electric and magnetic fields) and it is a two-coupled harmonic oscillators. In Section 4 of the Chapter four we presented the solution for the classical harmonic oscillator. As we observed in Chapter five, it is probable that the Lorentz’s theory (an electron is harmonically bound to the nucleus of the atom, following the equation of motion of a harmonic oscillator) used to elucidate the Zeeman effect was the basis for Planck’s theory on the thermal black body.
Applications of the Formalism-II
Published in Shabnam Siddiqui, Quantum Mechanics, 2018
A harmonic oscillator is a system that exhibits simple harmonic motion or periodic motion, a motion that repeats itself after equal intervals of time. Such a motion is caused by a restoring force, which is proportional to displacement of the oscillator and acts in a direction opposite to the displacement. Many systems such as spring, simple pendulum, vibrating string and molecular vibration can be approximated as simple harmonic oscillators. In classical physics, such systems are well understood. Therefore, the most natural question to ask is, what is a quantum mechanical simple harmonic motion? What are its properties? Its study is key to understanding the vibration of individual atoms in molecules and crystals. It is also very important for understanding particle properties of an electromagnetic wave. In this chapter, first we solve the Schrodinger equation for a harmonic oscillator using two methods, analytical method and algebraic method. Later, we discuss the quantum properties of the harmonic oscillator.
Introduction
Published in Eduard Naudascher, Donald Rockwell, Flow-Induced Vibrations, 2017
Eduard Naudascher, Donald Rockwell
Flow-induced vibration phenomena have been treated by a variety of engineering disciplines, each having its particular terminology. In an attempt to provide a unified overview, we propose the following definition of basic elements of flow-induced vibrations: Body oscillators;Fluid oscillators; andSources of excitation. Oscillators are defined herein as systems of structural or fluid mass that are acted upon by restoring forces if deflected from their equilibrium positions and undergo vibrations in conjunction with appropriate types of excitation. An engineering system will usually possess several potential oscillators and several sources of excitation. The first and most important task in the assessment of possible flow-induced vibrations is therefore to identify them.
Applications of Elzaki decomposition method to fractional relaxation-oscillation and fractional biological population equations
Published in Applied Mathematics in Science and Engineering, 2023
Lata Chanchlani, Mohini Agrawal, Rupakshi Mishra Pandey, Sunil Dutt Purohit, D. L. Suthar
In physical, chemical and biological processes, an oscillator is something that exhibits a rhythmic periodic reaction. Many real mechanical, radio-technical, biological and other things have oscillatory processes in which a slow smooth transition of an object’s status over a finite length of time shifts to an irregular change of status over an incredibly short period. The behaviour of a physical system returning to equilibrium after being disrupted provides the basis for a relaxation oscillation. A damped oscillating system is an oscillator that fades away over time owing to energy loss, such as a swinging pendulum, a weight on a spring or a resistor-inductor-capacitor circuit. Relaxation and damped oscillations are described by ordinary differential equations of order one and two, respectively.
Surge and heave hydrodynamic coefficients for a combination of a porous and a rigid cylinder in motion in finite ocean depth
Published in Waves in Random and Complex Media, 2021
Abhijit Sarkar, Swaroop Nandan Bora
Solving radiation problems for ocean waves yields the important hydrodynamic coefficients, namely, added mass and damping coefficients. These coefficients arise as the real and imaginary parts of the hydrodynamic reaction loads on the body due to the prescribed body motions. In physical sense, the added mass is the weight added to a system in a fluid due to the fact that an accelerating or decelerating body must move some volume of surrounding fluid with it as it moves. Damping is an influence within or upon an oscillatory system that has the effect of reducing, restricting or preventing its oscillations. The hydrodynamic forces in the x- and z-directions (i.e. for surge and heave motions) due to the motion of the cylinder in modes m = 1, 2 can be found out by integrating the corresponding pressure over the cylinder. For this configuration, only surge motion is considered. The following explains why heave motion is not considered for this problem:
Correlated motion of electrons in the He atom irradiated with coherent light
Published in Molecular Physics, 2018
It is known that the equation of motion of the Thouless parameters can be derived on the basis of the time-dependent variational principle [23,24]. As a method for obtaining the trajectories of the Thouless parameters, it does not seem to work well for the reason of difficulty of quantisation. The equation of motion of the Thouless parameters corresponds to classical mechanics of a certain fictitious system. In order to obtain eigenstates of the original quantum mechanical system, a process of quantisation is indispensable. The equation of motion usually results in that of non-linear coupled oscillators. Due to the existence of chaos, the semiclassical quantisation is extremely difficult. In other words, quantisation of the trajectory of the Thouless parameters belongs to an open problem. This is the background of the present study, in which the Thouless parameters are obtained from the Floquet wave function by the use of the conversion scheme specifically invented for the present issue.