Determine the Eigen Function of Schrodinger Equation with Non-Central Potential by Using NU Method

Author(s)
Hamdollah Salehi

ABSTRACT

So far, Schrodinger equation with central potential has been solved in different methods but solving this equation with non-central potentials is less dealt with. Solving such equations are way more difficult and complicated and a certain and limited number of non-central potentials can be solved. In this paper, we introduce one of the solvable kinds of such potentials and we will use NU method for solving Schrodinger equation and then by using this method we have calculated particular figures of its energy and function.

So far, Schrodinger equation with central potential has been solved in different methods but solving this equation with non-central potentials is less dealt with. Solving such equations are way more difficult and complicated and a certain and limited number of non-central potentials can be solved. In this paper, we introduce one of the solvable kinds of such potentials and we will use NU method for solving Schrodinger equation and then by using this method we have calculated particular figures of its energy and function.

Cite this paper

nullH. Salehi, "Determine the Eigen Function of Schrodinger Equation with Non-Central Potential by Using NU Method,"*Applied Mathematics*, Vol. 2 No. 8, 2011, pp. 999-1004. doi: 10.4236/am.2011.28138.

nullH. Salehi, "Determine the Eigen Function of Schrodinger Equation with Non-Central Potential by Using NU Method,"

References

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[2] R. Dutt, A. Gangopadhyaya and U. P Sukhatme, “Noncentral Potentials and Spherical Harmonics Using Supersymmetry and Shape Invariance,” American Journal of Physics, Vol. 65, 1997, pp. 400-403.

[3] Y. Aharonov and D. Bohn, “On the Measurement of Velocity of Relaivistic Particles,” Il Nuovo Cimento (1955-1965), Vol. 5, No. 3, 1957, pp. 429-439.

[4] B. M. Mandel, “Path Integral Solution of Noncentral Potential,” International Journal of Modern Physics A, Vol. 15, No. 9, 2000, pp. 1225-1238.

[5] A. F. Nikiforov and V. B. Uvarov, “Special Functions of Mathematical Physics Birkhauser,” Basel, 1988.

[6] H. F. Jones and R. J. Rivers, “Which Green Functions does the Path Integral for Quasi-Hermitian Hamiltonians Represent?” Physics Letters A, Vol. 373, No. 37, 2009, pp. 3304-3308. doi:10.1016/j.physleta.2009.07.034

[7] S. Sakoda, “Exactncess in the Path Integral of Coulomb Potential in One Space Dimension,” Modern Physics Letters A, Vol. 23, No. 36, 2008, pp. 3057-3076. doi:10.1142/S0217732308028491

[8] F. Cooper, J. Ginocchio and A. Khare, “Relationship between Suprsymmetry and Solvable Potentials,” Physical Review D, Vol. 36, No. 8, 1987, pp. 2458-2473. doi:10.1103/PhysRevD.36.2458

[9] R. Dutt, A. Khare and U. P. Sukhatme, “Is the Lowest Order Supersymmetric WKB Approximation Exact for All Shape Invariant Potentials,” American Journal of Physics, Vol. 56, No. 2, 1988, pp. 163-168. doi:10.1119/1.15697

[10] H. Katsura, H. Aoki and J. Math, “Exact Supersymmetry in the Relativistic Hydrogen Atom in General Dimension Superchange and Gerelized Johnson-Lippman Operator,” Physics, Vol. 47, 2006, pp. 032301.

[11] G. Arfken, “Mathematical Methods for Physics,” 3rd Edition, Academic Press, Waltham, 1985.

[1] B. Gonu and I. Zorba, “Supersymmeric Solutions of Non- central Potentials,” Physics Letters A, Vol. 269, No. 2-3, 2000, pp. 83-88. doi:10.1016/S0375-9601(00)00252-8

[2] R. Dutt, A. Gangopadhyaya and U. P Sukhatme, “Noncentral Potentials and Spherical Harmonics Using Supersymmetry and Shape Invariance,” American Journal of Physics, Vol. 65, 1997, pp. 400-403.

[3] Y. Aharonov and D. Bohn, “On the Measurement of Velocity of Relaivistic Particles,” Il Nuovo Cimento (1955-1965), Vol. 5, No. 3, 1957, pp. 429-439.

[4] B. M. Mandel, “Path Integral Solution of Noncentral Potential,” International Journal of Modern Physics A, Vol. 15, No. 9, 2000, pp. 1225-1238.

[5] A. F. Nikiforov and V. B. Uvarov, “Special Functions of Mathematical Physics Birkhauser,” Basel, 1988.

[6] H. F. Jones and R. J. Rivers, “Which Green Functions does the Path Integral for Quasi-Hermitian Hamiltonians Represent?” Physics Letters A, Vol. 373, No. 37, 2009, pp. 3304-3308. doi:10.1016/j.physleta.2009.07.034

[7] S. Sakoda, “Exactncess in the Path Integral of Coulomb Potential in One Space Dimension,” Modern Physics Letters A, Vol. 23, No. 36, 2008, pp. 3057-3076. doi:10.1142/S0217732308028491

[8] F. Cooper, J. Ginocchio and A. Khare, “Relationship between Suprsymmetry and Solvable Potentials,” Physical Review D, Vol. 36, No. 8, 1987, pp. 2458-2473. doi:10.1103/PhysRevD.36.2458

[9] R. Dutt, A. Khare and U. P. Sukhatme, “Is the Lowest Order Supersymmetric WKB Approximation Exact for All Shape Invariant Potentials,” American Journal of Physics, Vol. 56, No. 2, 1988, pp. 163-168. doi:10.1119/1.15697

[10] H. Katsura, H. Aoki and J. Math, “Exact Supersymmetry in the Relativistic Hydrogen Atom in General Dimension Superchange and Gerelized Johnson-Lippman Operator,” Physics, Vol. 47, 2006, pp. 032301.

[11] G. Arfken, “Mathematical Methods for Physics,” 3rd Edition, Academic Press, Waltham, 1985.