Eksempler på brug af Harmonic oscillator på Engelsk og deres oversættelser til Dansk
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For an example, consider a harmonic oscillator;
The proof of this proposition for a harmonic oscillator with a more general potential energy function is given in Particle Averaging.
The Hamiltonian operator for a harmonic oscillator is.
A Harmonic Oscillator A mass m subject to a restoring force proportional to its deviation x from equilibrium executes harmonic motion.
The heavy line is the probability density function for a classical harmonic oscillator.
The energy radiating atoms act as harmonic oscillators, which each has a frequency f.
Let us quantum transform the equation giving the classical-mechanical energy of a harmonic oscillator.
With the quantum assumption introduced by Planck, a harmonic oscillator can only take on discrete energies En given by.
As can be seen that heavy line is roughly the spatial average of the probability density function derived from the solution of Schrödinger's equation for a harmonic oscillator.
The graph below shows the probability density function for a harmonic oscillator with a principal quantum number of 60.
For an example, consider a harmonic oscillator; i.e., a physical system in which the restoring force on a particle is proportional to its deviation from equilibrium.
The heavy line is the time-spent probability density function for the harmonic oscillator of the same energy.
With the quantum assumption introduced by Planck, a harmonic oscillator can only take on discrete energies En given by:(1) where n is an energy quantum number, which can only take on the values 1, 2, 3, etc.
Max Planck used the following ad hoc assumptions:The energy radiating atoms act as harmonic oscillators, which each has a frequency f.
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In the traditional wave-quantum mechanics, a relatively complicated mathematical solution to Schrödinger's continuous wave equation- used on the harmonic oscillator- gives the values for the energies shown in 1.
So for any spatial averaging there is a level energy for a quantum mechanical harmonic oscillator such that the spatial average is equal to the time-spent probability density distribution for a classical harmonic oscillator.
For the classical/mechanical harmonic oscillator(i.e. a particle influenced by an elastic force) is valid that the mechanical energy(viz. the sum of the kinetic and the elastical potential energy) is proportional to the oscillation amplitude to the 2nd power.
The Verbos Electronics Harmonic Oscillator is the first module ever to incorporate eight outputs, translating the harmonics into sine waves. The Harmonic Oscillator module also features triangle, saw and square waves, making it ideal for sound design applications.
As the energy of the quantum harmonic oscillator increases fluctuations in probability density become more dense and hence no matter how short the interval over which they are averaged there will be some energy level at which the average is equal to the classical time-spent probability density function.