Search results
Results from the WOW.Com Content Network
The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics.
The case = is called the ground state, its energy is called the zero-point energy, and the wave function is a Gaussian. [22] The harmonic oscillator, like the particle in a box, illustrates the generic feature of the Schrödinger equation that the energies of bound eigenstates are discretized. [11]: 352
The phase velocity is the rate at which the phase of the wave propagates in space. The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.
In this theory, the wave equations and the wave functions have their place, but in a somewhat different guise. The main objects of interest are not the wave functions, but rather operators, so called field operators (or just fields where "operator" is understood) on the Hilbert space of states (to be described next section). It turns out that ...
A simulation of a wave packet incident on a potential barrier. In relative units, the barrier energy is 20, greater than the mean wave packet energy of 14. A portion of the wave packet passes through the barrier. The wave function of a physical system of particles specifies everything that can be known about the system. [8]
In the framework of the de Broglie–Bohm theory, the quantum potential is a term within the Schrödinger equation which acts to guide the movement of quantum particles. . The quantum potential approach introduced by Bohm [1] [2] provides a physically less fundamental exposition of the idea presented by Louis de Broglie: de Broglie had postulated in 1925 that the relativistic wave function ...
The measurements of the energy they lose in electron energy loss spectroscopy provides information about the chemistry and electronic structure of materials. Beams of electrons also lead to characteristic X-rays in energy dispersive spectroscopy which can produce information about chemical content at the nanoscale.
Both differential equations have the form of the general wave equation for waves propagating with speed , where is a function of time and location, which gives the amplitude of the wave at some time at a certain location: = This is also written as: = where denotes the so-called d'Alembert operator, which in Cartesian coordinates is given as