• In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force F proportional...
    34 KB (4,575 words) - 10:39, 7 December 2024
  • Thumbnail for Quantum harmonic oscillator
    The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary smooth potential can usually...
    44 KB (6,975 words) - 15:34, 13 November 2024
  • Thumbnail for Simple harmonic motion
    displacement from the fixed point is called simple harmonic motion. In the diagram, a simple harmonic oscillator, consisting of a weight attached to one end...
    15 KB (2,224 words) - 00:42, 28 November 2024
  • Thumbnail for Oscillation
    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 (3,045 words) - 05:32, 30 November 2024
  • two general types of electronic oscillators: the linear or harmonic oscillator, and the nonlinear or relaxation oscillator. The two types are fundamentally...
    67 KB (7,028 words) - 02:07, 3 December 2024
  • Thumbnail for Quantum mechanics
    model of the quantum harmonic oscillator uses an explicitly non-relativistic expression for the kinetic energy of the oscillator, and is thus a quantum...
    99 KB (12,087 words) - 23:57, 15 December 2024
  • Thumbnail for Resonance
    are modeled as harmonic oscillators near their equilibria, a derivation of the resonant frequency for a driven, damped harmonic oscillator is shown. An...
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  • Thumbnail for Anharmonicity
    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...
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  • -dimensional isotropic harmonic oscillators. That is, each particle in our ensemble can be treated as a simple harmonic oscillator. The Hamiltonian for...
    24 KB (3,887 words) - 18:56, 7 July 2024
  • 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
  • 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) - 14:10, 29 October 2024
  • 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...
    74 KB (10,234 words) - 19:25, 14 December 2024
  • Thumbnail for Torsion spring
    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
  • study and the classical limit. Consider the example of a simple harmonic oscillator initially at rest with amplitude A. Suppose that this system was...
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  • Thumbnail for Uncertainty principle
    by the uncertainty principle. Consider a one-dimensional quantum harmonic oscillator. It is possible to express the position and momentum operators in...
    139 KB (19,263 words) - 09:21, 16 December 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 (2,759 words) - 14:52, 2 November 2024
  • Thumbnail for Young Suh Kim
    Covariant Harmonic Oscillators and the Quark Model. Phys. Rev. D 8, 3521-3526 Kim, Y.S. & Noz, M.E. (1977). Covariant Harmonic Oscillators and the Parton...
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  • be adiabatic invariants. Given Planck's quantization rule for the harmonic oscillator, either condition determines the correct classical quantity to quantize...
    32 KB (4,836 words) - 02:22, 27 November 2024
  • Thumbnail for Equipartition theorem
    any type of harmonic oscillator, such as a pendulum, a vibrating molecule or a passive electronic oscillator. Systems of such oscillators arise in many...
    90 KB (11,957 words) - 18:25, 15 December 2024
  • Thumbnail for Nuclear shell model
    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 (4,119 words) - 16:59, 28 August 2024
  • Thumbnail for Clock
    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 (11,218 words) - 12:33, 29 November 2024
  • Thumbnail for Harmonic
    to call a  partial  a  harmonic,  the first being actual and the second being theoretical). Oscillators that produce harmonic partials behave somewhat...
    27 KB (2,368 words) - 10:37, 16 December 2024
  • Thumbnail for Hooke's law
    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) - 12:23, 6 December 2024
  • equation for a simple harmonic oscillator with frequency ω = g / L {\displaystyle \omega ={\sqrt {g/L}}} . A harmonic oscillator can be damped, often by...
    123 KB (15,545 words) - 02:31, 23 December 2024
  • practical obstacles in both cases. The Hamiltonian for the simple harmonic oscillator in one spatial dimension in the Wigner–Weyl representation is H =...
    27 KB (3,600 words) - 04:24, 25 October 2024
  • Thumbnail for Bertrand's theorem
    f(r)=-{\frac {dV}{dr}}=-{\frac {k}{r^{2}}}} . The second is the radial harmonic oscillator potential: V ( r ) = 1 2 k r 2 {\displaystyle V(r)={\frac {1}{2}}kr^{2}}...
    13 KB (2,536 words) - 15:03, 16 December 2024
  • Thumbnail for Wave function
    ) 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 (13,587 words) - 16:07, 13 December 2024
  • freedom of molecules towards its thermodynamic variables. A quantum harmonic oscillator has an energy spectrum characterized by: E j , n = ℏ ω j ( n j +...
    4 KB (773 words) - 15:52, 25 September 2024
  • Thumbnail for Quantum field theory
    promotion of a classical harmonic oscillator to a quantum harmonic oscillator. The displacement of a classical harmonic oscillator is described by x ( t...
    106 KB (14,793 words) - 17:15, 14 December 2024
  • may also refer to: Electronic oscillator Voltage-controlled oscillator, used in synthesizers Harmonic oscillator Oscillator (technical analysis), a method...
    937 bytes (107 words) - 13:12, 19 November 2024