Quantum mechanical in the context of Degeneracy pressure

A chemical bond is the association of atoms or ions to form molecules, crystals, and other structures. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds or through the sharing of electrons as in covalent bonds, or some combination of these effects. Chemical bonds are described as having different strengths: there are "strong bonds" or "primary bonds" such as covalent, ionic and metallic bonds, and "weak bonds" or "secondary bonds" such as dipole–dipole interactions, the London dispersion force, and hydrogen bonding.

Since opposite electric charges attract, the negatively charged electrons surrounding the nucleus and the positively charged protons within a nucleus attract each other. Electrons shared between two nuclei will be attracted to both of them. "Constructive quantum mechanical wavefunction interference" stabilizes the paired nuclei (see Theories of chemical bonding). Bonded nuclei maintain an optimal distance (the bond distance) balancing attractive and repulsive effects explained quantitatively by quantum theory.

Classical electromagnetism or classical electrodynamics is a branch of physics focused on the study of interactions between electric charges and currents using an extension of the classical Newtonian model. It is, therefore, a classical field theory. The theory provides a description of electromagnetic phenomena whenever the relevant length scales and field strengths are large enough that quantum mechanical effects are negligible. For small distances and low field strengths, such interactions are better described by quantum electrodynamics which is a quantum field theory.

Diamagnetism is the property of materials that are repelled by a magnetic field; an applied magnetic field creates an induced magnetic field in them in the opposite direction, causing a repulsive force. In contrast, paramagnetic and ferromagnetic materials are attracted by a magnetic field. Diamagnetism is a quantum mechanical effect that occurs in all materials; when it is the only contribution to the magnetism, the material is called diamagnetic. In paramagnetic and ferromagnetic substances, the weak diamagnetic force is overcome by the attractive force of magnetic dipoles in the material. The magnetic permeability of diamagnetic materials is less than the permeability of vacuum, μ₀. In most materials, diamagnetism is a weak effect which can be detected only by sensitive laboratory instruments, but a superconductor acts as a strong diamagnet because it entirely expels any magnetic field from its interior (the Meissner effect).

Diamagnetism was first discovered when Anton Brugmans observed in 1778 that bismuth was repelled by magnetic fields. In 1845, Michael Faraday demonstrated that it was a property of matter and concluded that every material responded (in either a diamagnetic or paramagnetic way) to an applied magnetic field. On a suggestion by William Whewell, Faraday first referred to the phenomenon as diamagnetic (the prefix dia- meaning through or across), then later changed it to diamagnetism.

Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly fluctuate in their lowest energy state as described by the Heisenberg uncertainty principle. Therefore, even at absolute zero, atoms and molecules retain some vibrational motion. Apart from atoms and molecules, the empty space of the vacuum also has these properties. According to quantum field theory, the universe can be thought of not as isolated particles but continuous fluctuating fields: matter fields, whose quanta are fermions (i.e., leptons and quarks), and force fields, whose quanta are bosons (e.g., photons and gluons). All these fields have zero-point energy. These fluctuating zero-point fields lead to a kind of reintroduction of an aether in physics since some systems can detect the existence of this energy. However, this aether cannot be thought of as a physical medium if it is to be Lorentz invariant such that there is no contradiction with Albert Einstein's theory of special relativity.

The notion of a zero-point energy is also important for cosmology, and physics currently lacks a full theoretical model for understanding zero-point energy in this context; in particular, the discrepancy between theorized and observed vacuum energy in the universe is a source of major contention. Yet according to Einstein's theory of general relativity, any such energy would gravitate, and the experimental evidence from the expansion of the universe, dark energy and the Casimir effect shows any such energy to be exceptionally weak. One proposal that attempts to address this issue is to say that the fermion field has a negative zero-point energy, while the boson field has positive zero-point energy and thus these energies somehow cancel out each other. This idea would be true if supersymmetry were an exact symmetry of nature; however, the Large Hadron Collider at CERN has so far found no evidence to support it. Moreover, it is known that if supersymmetry is valid at all, it is at most a broken symmetry, only true at very high energies, and no one has been able to show a theory where zero-point cancellations occur in the low-energy universe we observe today. This discrepancy is known as the cosmological constant problem and it is one of the greatest unsolved mysteries in physics. Many physicists believe that "the vacuum holds the key to a full understanding of nature".

In astrophysics and condensed matter physics, electron degeneracy pressure is a quantum mechanical effect critical to understanding the stability of white dwarf stars and metal solids. It is a manifestation of the more general phenomenon of quantum degeneracy pressure.

The term "degenerate" here is not related to degenerate energy levels, but to Fermi–Dirac statistics close to the zero-temperature limit (temperatures much smaller than the Fermi temperature, which for metals is about 10,000 K).

Nanotechnology is the manipulation of matter with at least one dimension sized from 1 to 100 nanometers (nm). At this scale, commonly known as the nanoscale, surface area and quantum mechanical effects become important in describing properties of matter. This definition of nanotechnology includes all types of research and technologies that deal with these special properties. It is common to see the plural form "nanotechnologies" as well as "nanoscale technologies" to refer to research and applications whose common trait is scale. An earlier understanding of nanotechnology referred to the particular technological goal of precisely manipulating atoms and molecules for fabricating macroscale products, now referred to as molecular nanotechnology.

Nanotechnology defined by scale includes fields of science such as surface science, organic chemistry, molecular biology, semiconductor physics, energy storage, engineering, microfabrication, and molecular engineering. The associated research and applications range from extensions of conventional device physics to molecular self-assembly, from developing new materials with dimensions on the nanoscale to direct control of matter on the atomic scale.

In organic chemistry, Hückel's rule predicts that a planar ring molecule will have aromatic properties if it has 4n + 2 π-electrons, where n is a non-negative integer. The quantum mechanical basis for its formulation was first worked out by physical chemist Erich Hückel in 1931. The succinct expression as the 4n + 2 rule has been attributed to W. v. E. Doering (1951), although several authors were using this form at around the same time.

In agreement with the Möbius–Hückel concept, a cyclic ring molecule follows Hückel's rule when the number of its π-electrons equals 4n + 2, although clearcut examples are really only established for values of n = 0 up to about n = 6. Hückel's rule was originally based on calculations using the Hückel method, although it can also be justified by considering a particle in a ring system, by the LCAO method and by the Pariser–Parr–Pople method.

In the physical sciences, the wavenumber (or wave number), also known as repetency, is the spatial frequency of a wave. Ordinary wavenumber is defined as the number of wave cycles divided by length; it is a physical quantity with dimension of reciprocal length, expressed in SI units of cycles per metre or reciprocal metre (m). Angular wavenumber, defined as the wave phase divided by time, is a quantity with dimension of angle per length and SI units of radians per metre. They are analogous to temporal frequency, respectively the ordinary frequency, defined as the number of wave cycles divided by time (in cycles per second or reciprocal seconds), and the angular frequency, defined as the phase angle divided by time (in radians per second).

In multidimensional systems, the wavenumber is the magnitude of the wave vector. The space of wave vectors is called reciprocal space. Wave numbers and wave vectors play an essential role in optics and the physics of wave scattering, such as X-ray diffraction, neutron diffraction, electron diffraction, and elementary particle physics. For quantum mechanical waves, the wavenumber multiplied by the reduced Planck constant is the canonical momentum.

A phonon is a quasiparticle, collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, specifically in solids and some liquids. In the context of optically trapped objects, the quantized vibration mode can be defined as phonons as long as the modal wavelength of the oscillation is smaller than the size of the object. A type of quasiparticle in physics, a phonon is an excited state in the quantum mechanical quantization of the modes of vibrations for elastic structures of interacting particles. Phonons can be thought of as quantized sound waves, similar to photons as quantized light waves.

The study of phonons is an important part of condensed matter physics. They play a major role in many of the physical properties of condensed matter systems, such as thermal conductivity and electrical conductivity, as well as in models of neutron scattering and related effects.

The cubical atom was an early atomic model in which electrons were positioned at the eight corners of a cube in a non-polar atom or molecule. This theory was developed in 1902 by Gilbert N. Lewis and published in 1916 in the article "The Atom and the Molecule" and used to account for the phenomenon of valency. Lewis' theory was based on Abegg's rule. It was further developed in 1919 by Irving Langmuir as the cubical octet atom. The figure below shows structural representations for elements of the second row of the periodic table.

Although the cubical model of the atom was soon abandoned in favor of the quantum mechanical model based on the Schrödinger equation, and is therefore now principally of historical interest, it represented an important step towards the understanding of the chemical bond. The 1916 article by Lewis also introduced the concept of the electron pair in the covalent bond, the octet rule, and the now-called Lewis structure.

Nanoelectromechanical systems (NEMS) are a class of devices integrating electrical and mechanical functionality on the nanoscale. NEMS form the next logical miniaturization step from so-called microelectromechanical systems, or MEMS devices. NEMS typically integrate transistor-like nanoelectronics with mechanical actuators, pumps, or motors, and may thereby form physical, biological, and chemical sensors. The name derives from typical device dimensions in the nanometer range, leading to low mass, high mechanical resonance frequencies, potentially large quantum mechanical effects such as zero point motion, and a high surface-to-volume ratio useful for surface-based sensing mechanisms. Applications include accelerometers and sensors to detect chemical substances in the air.