Inner-product theory calculations for some rational potentials in a three-dimensional system

1996 ◽  
Vol 74 (1-2) ◽  
pp. 4-9
Author(s):  
M. R. M. Witwit
Keyword(s):  
Energy Levels ◽  
Three Dimensional ◽  
Inner Product ◽  
Dimensional System ◽  
Product Technique ◽  
Special Cases ◽  
Wide Range ◽  
Perturbation Parameters ◽  
Three Dimensional System ◽  
Range Of Values

The energy levels of a three-dimensional system are calculated for the rational potentials,[Formula: see text]using the inner-product technique over a wide range of values of the perturbation parameters (λ, g) and for various eigenstates. The numerical results for some special cases agree with those of previous workers where available.

Energy levels of the Schrödinger equation for some rational potentials using the hypervirial method

1992 ◽  
Vol 70 (12) ◽  
pp. 1261-1266 ◽  
Author(s):  
M. R. M. Witwit ◽  
J. P. Killingbeck
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Padé Approximants ◽  
Numerical Results ◽  
Dimensional System ◽  
One Dimensional ◽  
Wide Range ◽  
Perturbation Parameters ◽  
Range Of Values

The energy levels of a one-dimensional system are calculated for the rational potentials, [Formula: see text] and [Formula: see text], with (2L = 4, 6). We use the hypervirial method and Padé approximants over a wide range of values of the perturbation parameters (α, g, λ) and for various states. The numerical results agree with those of previous workers where they are available.

scholarly journals Simplified wide-Range ultrasonic measurements using the sensor three-Dimensional system

2018 ◽  
Vol 26 (2) ◽  
pp. 100
Author(s):  
Seiichi Morokuma ◽  
Kana Maehara ◽  
Hikohiro Okawa ◽  
Kiyoko Kato ◽  
Yoshitaka Mine ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Dimensional System ◽  
Wide Range ◽  
Ultrasonic Measurements ◽  
Three Dimensional System

Article

1998 ◽  
Vol 76 (8) ◽  
pp. 609-620
Author(s):  
M RM Witwit ◽  
N A Gordon
Keyword(s):  
Large Class ◽  
Potential Function ◽  
Three Dimensional ◽  
Potential Functions ◽  
Numerical Calculations ◽  
Dimensional System ◽  
Perturbation Parameters ◽  
The Hill ◽  
Three Dimensional System

A determination of the eigenvalues for a three-dimensional system is made by expanding the potential function V(x,y,z;Z2, λ,β)= –Z2[x2+y2+z2]+λ {x4+y4+z4+2β[x2y2+x2z2+y2z2]}, around its minimum. In this paper the results of extensive numerical calculations using this expansion and the Hill-determinant approach are reported for a large class of potential functions and for various values of the perturbation parameters Z2, λ, and β. PACS No.:03.65

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