IMPACT OF COMPLEX-VALUED ENERGY FUNCTION SINGULARITIES ON THE BEHAVIOUR OF RAYLEIGH-SCHRÖDINGER PERTURBATION SERIES. H2CO MOLECULE VIBRATIONAL ENERGY SPECTRUM.

2015 ◽  
Author(s):  
Andrey Duchko ◽  
Alexandr Bykov
Keyword(s):  
Energy Spectrum ◽  
Energy Function ◽  
Vibrational Energy ◽  
Perturbation Series ◽  
Schrödinger Perturbation ◽  
Complex Valued

MODELS OF HOPFIELD-TYPE QUATERNION NEURAL NETWORKS AND THEIR ENERGY FUNCTIONS

2005 ◽  
Vol 15 (01n02) ◽  
pp. 129-135 ◽  
Author(s):  
MITSUO YOSHIDA ◽  
YASUAKI KUROE ◽  
TAKEHIRO MORI
Keyword(s):  
Neural Networks ◽  
Information Processing ◽  
Energy Function ◽  
Point Of View ◽  
Complex Numbers ◽  
Energy Functions ◽  
Fully Connected ◽  
Complex Valued

Recently models of neural networks that can directly deal with complex numbers, complex-valued neural networks, have been proposed and several studies on their abilities of information processing have been done. Furthermore models of neural networks that can deal with quaternion numbers, which is the extension of complex numbers, have also been proposed. However they are all multilayer quaternion neural networks. This paper proposes models of fully connected recurrent quaternion neural networks, Hopfield-type quaternion neural networks. Since quaternion numbers are non-commutative on multiplication, some different models can be considered. We investigate dynamics of these proposed models from the point of view of the existence of an energy function and derive their conditions for existence.

Analytical expressions for the energies of anharmonic oscillators

2000 ◽  
Vol 78 (9) ◽  
pp. 845-850
Author(s):  
F M Fernández ◽  
R H Tipping
Keyword(s):  
Perturbation Parameter ◽  
Bound State ◽  
Perturbation Series ◽  
Simple Expression ◽  
Branch Points ◽  
Anharmonic Oscillators ◽  
Large Coupling ◽  
Analytical Behavior ◽  
Schrödinger Perturbation ◽  
Analytical Expressions

We propose a systematic construction of algebraic approximants for the bound-state energies of anharmonic oscillators. The approximants are based on the Rayleigh-Schrödinger perturbation series and take into account the analytical behavior of the energies at large values of the perturbation parameter. A simple expression obtained from a low-order perturbation series compares favorably with alternative approximants. Present approximants converge in the large-coupling limit and are suitable for the calculation of the energy of highly excited states. Moreover, we obtain some branch points of the eigenvalues of the anharmonic oscillator as functions of the coupling constant. PACS No.: 03.65Ge

The vibrational energy spectrum of the 21Σg+ state of Li2

1984 ◽  
Vol 111 (4-5) ◽  
pp. 413-415 ◽  
Author(s):  
Daniel D. Konowalow ◽  
Lyn B. Ratcliff
Keyword(s):  
Energy Spectrum ◽  
Vibrational Energy
Sign in / Sign up

Export Citation Format

Share Document