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Matter waves are a central part of the theory of quantum mechanics, being half of wave–particle duality. At all scales where measurements have been practical, matter exhibits wave -like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave.
The evolution over time of the configuration of all particles is defined by a guiding equation. The evolution of the wave function over time is given by the Schrödinger equation. The theory is named after Louis de Broglie (1892–1987) and David Bohm (1917–1992).
This interaction is called an observation and is the essence of a measurement in quantum mechanics, which connects the wave function with classical observables such as position and momentum. Collapse is one of the two processes by which quantum systems evolve in time; the other is the continuous evolution governed by the Schrödinger equation .
Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms. [2]: 1.1 It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science.
This theory set the basis of wave mechanics. It was supported by Einstein, confirmed by the electron diffraction experiments of G P Thomson and Davisson and Germer, and generalized by the work of Erwin Schrödinger. From a philosophical viewpoint, this theory of matter-waves has contributed greatly to the ruin of the atomism of the past.
[32] [33] Supporters of collapse theories mostly dismiss this criticism as a misunderstanding of the theory, [34] [35] as in the context of dynamical collapse theories, the absolute square of the wave function is interpreted as an actual matter density. In this case, the tails merely represent an immeasurably small amount of smeared-out matter ...
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
A wave function for a single electron on 5d atomic orbital of a hydrogen atom. The solid body shows the places where the electron's probability density is above a certain value (here 0.02 nm −3): this is calculated from the probability amplitude. The hue on the colored surface shows the complex phase of the wave function.