A simple derivation of the addition theorems of the irregular solid harmonics, the Helmholtz harmonics, and the modified Helmholtz harmonics

1985 ◽  
Vol 26 (4) ◽  
pp. 664-670 ◽  
Author(s):  
E. Joachim Weniger ◽  
E. Otto Steinborn
Keyword(s):  
Addition Theorems ◽  
Simple Derivation ◽  
Irregular Solid Harmonics

Addition theorems for $${\mathcal {C}}^k$$ real functions and applications in ordinary differential equations

2021 ◽  
Author(s):  
Francisco Crespo ◽  
Salomón Rebollo-Perdomo ◽  
Jorge L. Zapata
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Addition Theorems ◽  
Real Functions

A Very Simple Derivation of Young's Law with Gravity Using a Cylindrical Meniscus

Langmuir ◽  
1997 ◽  
Vol 13 (26) ◽  
pp. 7299-7300 ◽  
Author(s):  
Yves Larher
Keyword(s):  
Simple Derivation

Simple derivation of the quantum mechanical virial theorem

1991 ◽  
Vol 59 (5) ◽  
pp. 476-476 ◽  
Author(s):  
T. C. Ernest Ma
Keyword(s):  
Virial Theorem ◽  
Quantum Mechanical ◽  
Simple Derivation

A Simple Derivation of Microstrip Transmission Line Equations

2009 ◽  
Vol 70 (1) ◽  
pp. 353-367 ◽  
Author(s):  
Lin Zhou ◽  
Gregory A. Kriegsmann
Keyword(s):  
Transmission Line ◽  
Simple Derivation ◽  
Microstrip Transmission Line

GENERAL FORMULA FOR THE SECOND VIRIAL COEFFICIENT

1961 ◽  
Vol 39 (11) ◽  
pp. 1563-1572 ◽  
Author(s):  
J. Van Kranendonk
Keyword(s):  
Phase Shift ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Resolvent Operators ◽  
Simple Derivation ◽  
Scattering Phase ◽  
Scattering Phase Shifts ◽  
Quantization Volume ◽  
Mechanical Expression ◽  
The Waves

A simple derivation is given of the quantum mechanical expression for the second virial coefficient in terms of the scattering phase shifts. The derivation does not require the introduction of a quantization volume and is based on the identity R(z)−R0(z) = R0(z)H1R(z), where R0(z) and R(z) are the resolvent operators corresponding to the unperturbed and total Hamiltonians H0 and H0 + H1 respectively. The derivation is valid in particular for a gas of excitons in a crystal for which the shape of the waves describing the relative motion of two excitons is not spherical, and, in general, varies with varying energy. The validity of the phase shift formula is demonstrated explicitly for this case by considering a quantization volume with a boundary the shape of which varies with the energy in such a way that for each energy the boundary is a surface of constant phase. The density of states prescribed by the phase shift formula is shown to result if the enclosed volume is required to be the same for all energies.

Addition theorems for solid harmonics and the second Born amplitudes

1995 ◽  
Vol 28 (24) ◽  
pp. L769-L774 ◽  
Author(s):  
S Chakrabarti ◽  
D P Dewangan
Keyword(s):  
Addition Theorems

Simple Derivation of the Bloch Equation

1966 ◽  
Vol 34 (12) ◽  
pp. 1164-1168 ◽  
Author(s):  
D. ter Haar
Keyword(s):  
Bloch Equation ◽  
Simple Derivation
Sign in / Sign up

Export Citation Format

Share Document