New summation expressions obtained by combining perturbation theory formalisms

References

• Merzbacher , E. 1970 . Quantum Mechanics , 413 – 413 . New York : Wiley .
   Google Scholar
• Kim , I. W. and Sukhatme , U. P. 1992 . Alternative approach to non-relativistic perturbation theory . J. Phys. A: Math. Gen. , 25 : L647 – L650 .
   Google Scholar
• Aharonov , Y. and Au , C. K. 1979 . New approach to perturbation theory . Phys. Rev. Lett. , 42 : 1582 – 1585 .
   Web of Science ®Google Scholar
• Aharonov , Y. and Au , C. K. 1979 . Gauge invariance and pseudoperturbations . Phys. Rev. , A 20 : 1553 – 1562 .
   Google Scholar
• Imbo , T. and Sukhatme , U. P. 1984 . Logarithmic perturbation expressions in nonrelativistic quantum mechanics . Am. J. Phys. , 52 : 140 – 146 .
   Google Scholar
• Au , C. K. , Chan , K. L. , Chow , C. K. , Chu , C. S. and Young , K. 1991 . Excited bound state logarithmic perturbation theory without nodes . J. Phys. A: Math. Gen. , 24 : 3837 – 3858 .
   Google Scholar
• Dalgarno , A. and Lewis , J. T. 1955 . The exact calculation of long-range forces between atoms by perturbation theory . Proc. R. Soc. , 233 : 70 – 74 .
   Google Scholar
• Schwartz , C. 1959 . Calculations in Schrödinger perturbation theory . Ann. Phys. , 2 : 156 – 169 .
   Web of Science ®Google Scholar
• Schwartz , C. 1959 . Uses of approximate wavefunctions . Ann. Phys. , 2 : 170 – 177 .
   Web of Science ®Google Scholar
• Mavromatis , H. A. 1991 . The Dalgarno-Lewis summation technique: Some comments and examples . Am. J. Phys. , 59 : 738 – 744 .
   Web of Science ®Google Scholar
• Jolley , L. B. W. 1961 . Summation of Series , 70 – 70 . Dover Publications .
   Google Scholar
• Gradshteyn , I. S. and Ryzhik , I. M. 1980 . Tables of Integrals, Series and Products , 7 – 7 . New York : Academic Press . prepared by A. Jeffrey
   Google Scholar
• Mathews , J. and Walker , R. L. 1970 . Mathematical Methods of Physics , 65 – 65 . Addison-Wesley Co. .
   Google Scholar
• Mathematica S. Wolfram Research, Inc. P. O. Box 6059 Champaign, Illinois 1998
   Google Scholar