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Coulomb Functions
In mathematics, a Coulomb wave function is a solution of the Coulomb wave equation, named after Charles-Augustin de Coulomb. They are used to describe the behavior of charged particles in a Coulomb potential and can be written in terms of confluent hypergeometric functions or Whittaker functions of imaginary argument. Coulomb wave equation The Coulomb wave equation for a single charged particle of mass m is the Schrödinger equation with Coulomb potential :\left(-\hbar^2\frac+\frac\right) \psi_(\vec) = \frac \psi_(\vec) \,, where Z=Z_1 Z_2 is the product of the charges of the particle and of the field source (in units of the elementary charge, Z=-1 for the hydrogen atom), \alpha is the fine-structure constant, and \hbar^2k^2/(2m) is the energy of the particle. The solution – Coulomb wave function – can be found by solving this equation in parabolic coordinates :\xi= r + \vec\cdot\hat, \quad \zeta= r - \vec\cdot\hat \qquad (\hat = \vec/k) \,. Depending on the boundary conditions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Irregular Coulomb Wave Function G Plotted From 0 To 20 With Repulsive And Attractive Interactions In Mathematica
Irregular, irregulars or irregularity may refer to any of the following: Astronomy * Irregular galaxy * Irregular moon * Irregular variable, a kind of star Language * Irregular inflection, the formation of derived forms such as plurals in unpredictable ways ** Irregular verb Law * Against regulations * In canon law, an irregularity is an impediment for the Catholic priesthood or for exercising orders already received Mathematics * Irregularity of a surface * Irregularity of distributions * Irregularity index Medicine * Irregular bone * Arrhythmia, also known as an irregular heartbeat * Constipation, also called "irregularity" Other * ''The Irregulars'', a 2021 Netflix series * Accounting irregularity * Irregular military * Irregular chess opening See also * Anomaly (other) * Baker Street Irregulars * Regular (other) The term regular can mean normal or in accordance with rules. It may refer to: People * Moses Regular (born 1971), America fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fine-structure Constant
In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Greek letter ''alpha''), is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between elementary charged particles. It is a dimensionless quantity, independent of the system of units used, which is related to the strength of the coupling of an elementary charge ''e'' with the electromagnetic field, by the formula . Its numerical value is approximately , with a relative uncertainty of The constant was named by Arnold Sommerfeld, who introduced it in 1916 Equation 12a, ''"rund 7·" (about ...)'' when extending the Bohr model of the atom. quantified the gap in the fine structure of the spectral lines of the hydrogen atom, which had been measured precisely by Michelson and Morley in 1887. Definition In terms of other fundamental physical constants, may be defined as: \alpha = \frac = \frac , where * is the elementary char ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
