scholarly journals Exact solution of inverse-square-root potential V(r)=−αr

2016 ◽  
Vol 373 ◽  
pp. 207-215 ◽  
Author(s):  
Wen-Du Li ◽  
Wu-Sheng Dai
Keyword(s):  
Exact Solution ◽  
Square Root ◽  
Root Potential

scholarly journals Exact solution of the 1D Dirac equation for the inverse-square-root potential 1/x$1/\sqrt{x}$

2020 ◽  
Vol 75 (8) ◽  
pp. 771-779 ◽  
Author(s):  
Artur M. Ishkhanyan
Keyword(s):  
Exact Solution ◽  
Dirac Equation ◽  
State Energy ◽  
Scalar Fields ◽  
Bound State ◽  
Hermite Functions ◽  
Square Root ◽  
Energy Eigenvalues ◽  
Root Potential ◽  
Pseudo Scalar

AbstractWe present the exact solution of the 1D Dirac equation for the inverse-square-root potential $1/\sqrt{x}$ for several configurations of vector, pseudo-scalar, and scalar fields. Each fundamental solution of the problem can be written as an irreducible linear combination of two Hermite functions of a scaled and shifted argument. We derive the exact equations for bound-state energy eigenvalues and construct accurate approximations for the energy spectrum.

The «square-root» potential and the charmonium

1978 ◽  
Vol 22 (17) ◽  
pp. 679-684 ◽  
Author(s):  
H. Freitas de Carvalho ◽  
R. Chanda ◽  
A. Brandão D'Oliveira
Keyword(s):  
Square Root ◽  
Root Potential
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