This premise, commonly referred to as the wave function
, has been used more as a mathematical tool than a representation of actual quantum particles," said David Arvidsson-Shukur, a Ph.
Our Fundamental Physical Space: An Essay on the Metaphysics of the Wave Function
, EDDY KEMING CHEN
The wave function
[psi] has four components and is expressed as a 4-1 matrix.
It will combine an optical cavity for high efficiency optical detection, and high optical resolution optics allowing for manipulations and patterning at the scale of the wave function
of individual particles.
For the mathematical obtaining of the wave function
([psi]-function) with respect to the atom of substance, he received the corresponding partial differential equation of the second order (in the history of physics is entered as <<Schrodinger equation>> [3, 6]), which describes the behavior of bound electrons in the well-known to him planetary-nuclear model of the atom [4, 12, 13].
([psi]) is a fundamental concept in quantum mechanics and is a description of the quantum state of a system.
In contrast, in an astonishing achievement in his third article, Schroedinger not only analogously solved the differential equation for the hydrogen atom in paraboloidal coordinates  but also developed a perturbation theory and calculated the intensities of spectral lines; in a fourth part , on incorporating time as a variable, he eliminated the energy parameter from the partial-differential equation, producing a temporal dependence in the resulting wave function
Combining (39) and (40) with already computed static parts of the wave function
(21) and (22) as well as multiplying the respective components with the e factor which sets the wave function
back into a non-rotating coordinate system (see (34)), we receive the exact solutions to the initial Schrodinger equation (27)
Instead, they occur in an uncertain, non-deterministic, probabilistic wave function
around the nucleus, or even through it.
Van Kampen emphasizes that the wave function
[psi], which obeys the Schrodinger equation, is not observed directly.
For atomic and molecular systems, his calculation is based on the fact that the wave function
and geometric elements of the wave described by the Schrodinger equation are mathematical objects that describe the same physical system and depend on its constants of motion.
Compared with the time-splitting Fourier-spectral method, the time-splitting Chebyshev- spectral method is unnecessary to treat the wave function
as periodic and holds the smoothness of the wave function