Simple derivation of equal spacing rule in masses in decuplet by current commutators

1968 ◽  
Vol 25 (3) ◽  
pp. 321-323
Author(s):  
Subir Kumar Bose
Keyword(s):  
Simple Derivation ◽  
Spacing Rule ◽  
Equal Spacing

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.

Simple Derivation of the Bloch Equation

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

New Self-Organized Nanostructure: Chain of Crystalline-Silicon Nanospheres

1999 ◽  
Vol 571 ◽  
Author(s):  
H. Kohno ◽  
S. Takeda ◽  
T. Iwasaki
Keyword(s):  
Amorphous Silica ◽  
Crystalline Silicon ◽  
The Self ◽  
Self Organized ◽  
Equal Spacing

ABSTRACTWe have grown chains of crystalline-Si nanospheres: the crystalline-Si nanospheres of about 10 nm in diameter are supported in amorphous silica and carbon at a nearly equal spacing by a self-organized process. The self-organized phenomenon was attributed to the periodic instability of catalyst on the top of growing wire and oxidization during the growth of nanowires.

A Simple Synthesis Method for Spherical 4R Linkages Reaching Four Positions

2011 ◽  
Vol 199-200 ◽  
pp. 1236-1239 ◽  
Author(s):  
Tong Yang ◽  
Jian You Han ◽  
Lai Rong Yin
Keyword(s):  
Matrix Method ◽  
Synthesis Method ◽  
Simple Synthesis ◽  
Simple Derivation ◽  
Derivation Method ◽  
Curve Equation ◽  
Linkage Synthesis

For spherical 4R linkage synthesis reaching four specified task positions, we introduce a simple derivation method of spherical Burmester curve equation by employing a displacement matrix method. Then we presented a method to calculate the coordinates of circle and center points, so the spherical Burmester curves can be drawn by the software developed.

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