In fields like computational chemistry and solid-state and condensed matter physics the so-called atomic orbitals, or spin-orbitals, as they appear in textbooks[1][2][3] on quantum physics, are often partially replaced by cubic harmonics for a number of reasons. These harmonics are usually named tesseral harmonics in the field of condensed matter physics in which the name kubic harmonics rather refers to the irreducible representations in the cubic point-group. [4]
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Albert Messiah (1999). Quantum Mechanics. Dover Publications. ISBN 0-486-40924-4.
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Stephen Gasiorowicz (1974). Quantum Physics. Wiley & Sons. ISBN 0-471-29281-8.
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Eugen Merzbacher (1961). Quantum Mechanics. Wiley & Sons. ISBN 0-471-59670-1.
often partially replaced by cubicharmonics for a number of reasons. These harmonics are usually named tesseral harmonics in the field of condensed matter...
related to Spherical harmonics. Cubicharmonic (often used instead of spherical harmonics in computations) Cylindrical harmonics Spherical basis Spinor...
cubicharmonic orbitals straightforwardly. The table expresses the matrix elements as functions of LCAO two-centre bond integrals between two cubic harmonic...
In mathematics, the harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means. It is sometimes appropriate for...
arithmetic mean and the harmonic mean. For all positive data sets containing at least one pair of unequal values, the harmonic mean is always the least...
_{y},\sigma _{z}\rbrace } can be called cubic super basis. Another commonly used super basis is spherical harmonic super basis which is built by replacing...
3-dimensional spherical harmonics. These shapes are not unique, and any linear combination is valid, like a transformation to cubicharmonics, in fact it is possible...
Harmonic balance is a method used to calculate the steady-state response of nonlinear differential equations, and is mostly applied to nonlinear electrical...
mathematics, a harmonic divisor number or Ore number is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor...
Vibrational spectroscopy (molecular vibration) List of small groups Cubicharmonics Drago, Russell S. (1977). Physical Methods in Chemistry. W.B. Saunders...
45\times 50\times 75)^{\frac {1}{5}}={\sqrt[{5}]{24\;300\;000}}=30.} The harmonic mean is an average which is useful for sets of numbers which are defined...
The cubic mean (written as x ¯ c u b i c {\displaystyle {\bar {x}}_{\mathrm {cubic} }} ) is a specific instance of the generalized mean with p = 3 {\displaystyle...
free space has been estimated to be 10−9 joules (10−2 ergs), or ~5 GeV per cubic meter. However, in quantum electrodynamics, consistency with the principle...
quadrature; physics, where they give rise to the eigenstates of the quantum harmonic oscillator; and they also occur in some cases of the heat equation (when...
a specific requirement that the harmonic content of the original signal be preserved without creating aliased harmonic content of the original signal above...
as the piezoelectric effect and the frequency doubling effect (second-harmonic generation). In addition, in such crystals, one-photon absorption (OPA)...
in the College of Letters and Sciences. His research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic...
and the points of one pair are called harmonic conjugates with respect to the other pair. 2. A harmoniccubic is an elliptic curve with j-invariant 1728...
motion of a damped oscillator with a more complex potential than in simple harmonic motion (which corresponds to the case β = δ = 0 {\displaystyle \beta =\delta...
displacement of gas by the pistons moving in the cylinders usually measured in cubic centimetres (cm3 or cc) or litres (l) or (L) (US: liter). For example, for...
tensor Σ {\displaystyle \mathbf {\Sigma } } . The elasticity tensor of a cubic crystal has components C i j k l = λ g i j g k l + μ ( g i k g j l + g i...
approximation for the vibrational structure of the molecule than the quantum harmonic oscillator because it explicitly includes the effects of bond breaking...
also present, i.e. lattice vibrations are nonlinear even in the case of harmonic interatomic potential. This nonlinearity contributes to thermal expansion...
include as special cases the Pythagorean means (arithmetic, geometric, and harmonic means). If p is a non-zero real number, and x 1 , … , x n {\displaystyle...
atoms are effectively screened. Secondly, the potentials V are treated as harmonic potentials. This is permissible as long as the atoms remain close to their...
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