In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force F proportional... 33 KB (4,573 words) - 07:57, 18 February 2024 |
The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually... 43 KB (6,825 words) - 00:02, 21 April 2024 |
Oscillation (redirect from Oscillator) three dimensions, harmonic oscillators behave similarly to one dimension. The simplest example of this is an isotropic oscillator, where the restoring... 21 KB (3,037 words) - 04:33, 6 December 2023 |
two general types of electronic oscillators: the linear or harmonic oscillator, and the nonlinear or relaxation oscillator. The two types are fundamentally... 61 KB (6,588 words) - 20:45, 17 April 2024 |
harmonic oscillators near their equilibria, this section begins with a derivation of the resonant frequency for a driven, damped harmonic oscillator.... 59 KB (7,899 words) - 04:50, 25 March 2024 |
Quantum mechanics (section Harmonic oscillator) model of the quantum harmonic oscillator uses an explicitly non-relativistic expression for the kinetic energy of the oscillator, and is thus a quantum... 98 KB (12,063 words) - 09:49, 28 March 2024 |
study and the classical limit. Consider the example of a simple harmonic oscillator initially at rest with amplitude A. Suppose that this system was... 9 KB (1,380 words) - 10:14, 9 July 2023 |
Anharmonicity (redirect from Anharmonic oscillator) system from being a harmonic oscillator. An oscillator that is not oscillating in harmonic motion is known as an anharmonic oscillator where the system can... 12 KB (1,231 words) - 12:29, 11 February 2024 |
Ladder operator (section Harmonic oscillator) operators in quantum mechanics are in the formalisms of the quantum harmonic oscillator and angular momentum. There is a relationship between the raising... 24 KB (4,501 words) - 22:41, 14 February 2024 |
Uncertainty principle (redirect from Uncertainty theorems in harmonic analysis) uncertainty principle. (Refs ) Consider a one-dimensional quantum harmonic oscillator. It is possible to express the position and momentum operators in... 138 KB (19,097 words) - 14:56, 30 March 2024 |
applications in quantum mechanics, notably in the study of quantum harmonic oscillators and many-particle systems. An annihilation operator (usually denoted... 25 KB (4,461 words) - 17:12, 16 March 2024 |
Schrödinger equation (section Harmonic oscillator) the zero-point energy, and the wave function is a Gaussian. The harmonic oscillator, like the particle in a box, illustrates the generic feature of the... 73 KB (10,110 words) - 08:19, 21 April 2024 |
Torsion spring (section Torsional harmonic oscillators) Their behavior is analogous to translational spring-mass oscillators (see Harmonic oscillator Equivalent systems). The general differential equation of... 19 KB (2,367 words) - 03:22, 1 April 2024 |
-dimensional isotropic harmonic oscillators. That is, each particle in our ensemble can be treated as a simple harmonic oscillator. The Hamiltonian for... 23 KB (3,806 words) - 14:36, 7 March 2024 |
sine waves are commonly seen in science and engineering, wherever a harmonic oscillator is losing energy faster than it is being supplied. A true sine wave... 20 KB (2,721 words) - 19:56, 1 January 2024 |
Clock (section Oscillator) semiconductor devices. The timekeeping element in every modern clock is a harmonic oscillator, a physical object (resonator) that vibrates or oscillates at a particular... 96 KB (11,198 words) - 05:28, 25 April 2024 |
to call a partial a harmonic, the first being actual and the second being theoretical). Oscillators that produce harmonic partials behave somewhat... 24 KB (2,206 words) - 06:58, 30 January 2024 |
potential with a shape somewhere between the square well and the harmonic oscillator. To this potential, a spin-orbit term is added. Even so, the total... 30 KB (4,054 words) - 06:08, 1 March 2024 |
be adiabatic invariants. Given Planck's quantization rule for the harmonic oscillator, either condition determines the correct classical quantity to quantize... 32 KB (4,607 words) - 17:11, 9 April 2024 |
Newton's laws of motion (section Harmonic motion) equation for a simple harmonic oscillator with frequency ω = g / L {\displaystyle \omega ={\sqrt {g/L}}} . A harmonic oscillator can be damped, often by... 121 KB (15,363 words) - 05:12, 4 April 2024 |
of light modes, which are harmonic oscillators. Examples of Wigner-function time evolutions in a quantum harmonic oscillator A coherent state. Combined... 36 KB (5,025 words) - 16:40, 14 April 2024 |
quantum harmonic oscillator is a well-known topic in quantum mechanical courses. We digress and say a few words about it. The harmonic oscillator Hamiltonian... 25 KB (4,783 words) - 19:57, 23 January 2024 |
Aromatic ring current (redirect from Harmonic Oscillator Model of Aromaticity) especially useful for polycyclic compounds. Yet another method called the harmonic oscillator model of aromaticity (HOMA) is defined as a normalized sum of squared... 9 KB (1,050 words) - 04:36, 19 February 2024 |
practical obstacles in both cases. The Hamiltonian for the simple harmonic oscillator in one spatial dimension in the Wigner–Weyl representation is H =... 26 KB (3,531 words) - 08:58, 7 November 2023 |
Wave function (section Quantum harmonic oscillator) ) determines in which basis the description is easiest. For the harmonic oscillator, x and p enter symmetrically, so there it does not matter which description... 99 KB (13,534 words) - 13:10, 15 April 2024 |
Hooke's law (section Harmonic oscillator) mass m attached to the end of a spring is a classic example of a harmonic oscillator. By pulling slightly on the mass and then releasing it, the system... 56 KB (9,420 words) - 14:07, 21 December 2023 |
freedom of molecules towards its thermodynamic variables. A quantum harmonic oscillator has an energy spectrum characterized by: Ej,n=ℏωj(nj+12){\displaystyle... 4 KB (683 words) - 04:18, 24 May 2022 |