Rydberg constant
(0.001 seconds)
1—10 of 435 matching pages
1: 33.22 Particle Scattering and Atomic and Molecular Spectra
…
►
§33.22(i) Schrödinger Equation
►With denoting here the elementary charge, the Coulomb potential between two point particles with charges and masses separated by a distance is , where are atomic numbers, is the electric constant, is the fine structure constant, and is the reduced Planck’s constant. The reduced mass is , and at energy of relative motion with relative orbital angular momentum , the Schrödinger equation for the radial wave function is given by … ►For and , the electron mass, the scaling factors in (33.22.5) reduce to the Bohr radius, , and to a multiple of the Rydberg constant, ► . …2: Bibliography H
…
►
The combination of -matrix and complex coordinate methods: Application to the diamagnetic Rydberg spectra of Ba and Sr.
J. Phys. B 26 (12), pp. 1775–1790.
►
Formulae for growth factors in expanding universes containing matter and a cosmological constant.
Monthly Notices Roy. Astronom. Soc. 322 (2), pp. 419–425.
…
►
Note on Dr. Vacca’s series for
.
Quart. J. Math. 43, pp. 215–216.
…
3: Bibliography
…
►
Tables of for Complex Argument.
Pergamon Press, New York.
…
►
Numerical Tables for Angular Correlation Computations in -, - and -Spectroscopy: -, -, -Symbols, F- and -Coefficients.
Landolt-Börnstein Numerical Data and Functional Relationships
in Science and Technology, Springer-Verlag.
…
►
Multichannel Rydberg spectroscopy of complex atoms.
Reviews of Modern Physics 68, pp. 1015–1123.
4: 3.12 Mathematical Constants
§3.12 Mathematical Constants
►The fundamental constant …Other constants that appear in the DLMF include the base of natural logarithms …see §4.2(ii), and Euler’s constant … ►For access to online high-precision numerical values of mathematical constants see Sloane (2003). …5: 30.1 Special Notation
…
►
►
►The main functions treated in this chapter are the eigenvalues and the spheroidal wave functions , , , , and , .
…Meixner and Schäfke (1954) use , , , for , , , , respectively.
…
►Flammer (1957) and Abramowitz and Stegun (1964) use for , for , and
…where is a normalization constant determined by
…
real variable. Except in §§30.7(iv), 30.11(ii), 30.13, and 30.14, . | |
… | |
arbitrary small positive constant. |
6: 16.15 Integral Representations and Integrals
7: 32.9 Other Elementary Solutions
…
►with , , , and arbitrary constants.
…
►with an arbitrary constant, which is solvable by quadrature.
…
►with and arbitrary constants.
…
►with an arbitrary constant, which is solvable by quadrature.
…
►with and arbitrary constants.
…
8: 5.17 Barnes’ -Function (Double Gamma Function)
…
►
…
►Here is the Bernoulli number (§24.2(i)), and is Glaisher’s constant, given by
►
5.17.6
…
►
5.17.7
…
►For Glaisher’s constant see also Greene and Knuth (1982, p. 100) and §2.10(i).
9: 30.5 Functions of the Second Kind
…
►Other solutions of (30.2.1) with , , and are
►
30.5.1
.
…
►
30.5.2
…
►
30.5.4
►with as in (30.11.4).
…