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For very small particle diameter the latter is locally a constant whose value is given by the undisturbed Eulerian field evaluated at the location of the particle center, () = ((),). The small particle size also implies that the disturbed flow can be found in the limit of very small Reynolds number, leading to a drag force given by Stokes' drag .
A modified exchange operator is defined in the Hartree–Fock method of quantum chemistry, in order to estimate the exchange energy arising from the exchange statistics described above. In this method, one often defines an energetic exchange operator as:
A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 10 13 Hz to approximately 10 14 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm −1 and wavelengths of approximately 30 to 3 μm.
Molecular physics, while closely related to atomic physics, also overlaps greatly with theoretical chemistry, physical chemistry and chemical physics. [4] Both subfields are primarily concerned with electronic structure and the dynamical processes by which these arrangements change. Generally this work involves using quantum mechanics.
The first equation comes from Newton's laws of motion; the force acting on each particle in the system can be calculated as the negative gradient of (). For every time step, each particle's position X {\displaystyle X} and velocity V {\displaystyle V} may be integrated with a symplectic integrator method such as Verlet integration .
Thus, the dynamics of particle motion can be treated classically, and the equations of motion are time-reversible. As a simplifying assumption, the particles are usually assumed to have the same mass as one another; however, the theory can be generalized to a mass distribution, with each mass type contributing to the gas properties ...
The double-slit experiment for a classical particle, a wave, and a quantum particle demonstrating wave-particle duality In the double-slit experiment, as originally performed by Thomas Young in 1803, [ 32 ] and then Augustin Fresnel a decade later, [ 32 ] a beam of light is directed through two narrow, closely spaced slits, producing an ...
In quantum mechanics a free particle has as state function a plane wave function, which is a non-square-integrable function of well-defined momentum. The kinetic energy of this particle can take any positive value. The position of the COM is uniformly probable everywhere, in agreement with the Heisenberg uncertainty principle.
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