Exact solution of nonrelativistic Schrodinger equation for certain central physical potential
Creators
- 1. Kaiserslautern, Univ. (Germany). Fachbereich Physik
- 2. Gorakhpur, Univ. (India). Dep. of Physics
Description
It is obtained here a class/classes of exact solution of the nonrelativistic Schrodinger equation for certain central potentials of physical interest by using proper ansatz/ansatze. The explicit expressions of energy eigenvalue and eigenfunction are obtained for each solution. These solutions are valid when for, in general, each solutions an interrelation between the parameters of the potential and the orbital-angular-momentum quantum number l is satisfied. These solutions, besides having an aesthetic appeal, can be used as benchmark to test the accuracy of nonperturbative methods, which sometimes yield wrong results, of solving the Schrodinger equation. The exact solution for the following central potentials, which are relevant in different areas of physics, have been obtained: 1) V(r)=ar6 + br4 + cr2; 2) V(r)=ar2 + br + c/r; 3) V(r)=r2 + λr2/(1+gr2); 4) V(r)= a/r + b/(r+λ); 5a) V(r)=a/r + b/r2+c/r3+d/r4; 5)b V(r)=a/r2 + b/r2 + c/r4 + d/r6; 6a) V(r)=a/r1/2 + b/r3/2; 6b) V(r)=ar2/3 + br-2/3 + cr-4/3
Additional details
Publishing Information
- Journal Title
- Nuovo Cimento. B
- Journal Volume
- 113B
- Journal Issue
- 3
- Journal Page Range
- p. 299-328
- ISSN
- 0369-3554
- CODEN
- NCIBAW
INIS
- Country of Publication
- Italy
- Country of Input or Organization
- Italy
- INIS RN
- 29055583
- Subject category
- S71: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS;
- Quality check status
- Yes
- Descriptors DEI
- ANALYTICAL SOLUTION; MATHEMATICS; MECHANICS; QUANTUM MECHANICS; SCHROEDINGER EQUATION;
- Descriptors DEC
- DIFFERENTIAL EQUATIONS; EQUATIONS; MECHANICS; PARTIAL DIFFERENTIAL EQUATIONS; WAVE EQUATIONS;