next up previous contents
Next: About this document ... Up: Quantization as an Eigenvalue Problem Previous: Survey

Bibliography

1
E. Schrödinger, Ahhandlungen zur Wellenmechanik, Barth, Leipzig, 1927.

2
M. Born and P. Jordan, Elementare Quantenmechanik, Springer Verlag, Berlin and New York, 1930.

3
P. A. M. Dirac, The Principles of Quantum Mechanics, Oxford Univ. Press (Clarendon), London and New York, 1958.

4
J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton Univ. Press, Princelon, New Jersey, 1955.

5
J. R. Oppenheimer, ``Three notes on the quantum theory of aperiodic effects,'' Phys Rev. 13. 66-81 (1928).

6
E. C. Kemble, The Fundamental Principles of Quantum Mechanics, p. 163. McGraw-Hill, New York, 1937.

7
H. Weyl, ``Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungcn willlkürlichcr Funktionen.'' Math. Ann. 68, 220 269 (1910).

8
E. C. Titchmarsh, Eigenfunction Expansions Associatled with Second-Order Differential Equations, Oxford Univ Press (Clarendon), London and New York, (Pt. I) 1946. (Pt II) 1958.

9
E. A Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955

10
N. Dunford and J. T. Schwartz, Linear Operators Wiley (Inlerscicnce). New York (Pt. 1: General Theory) 1958. (Pt. II: Spectral Theory) 1963, (Pt. III: Spectral Operators) 1971.

11
An account of his work will be found in: V. de Alfaro and T Regge, Potential Scattering, North Holland Publ., Amsterdam. 1965.

12
G. Green, ``An essay on the application of mathematical analysis to the theories of electricity and magnetism (published at Nottingham, in 1828)'' In Mathematical Papers of the late George Green (N. M. Ferrers, ed.) Libr. Sci , Hermann. Paris. 1903.

13
B. L. Coulter and C. G. Adler, ``The relativistic. one-dimensional square potential,'' Amer J. Phys. 39, 305-309 (1971).

14
B. W. Roos and W. C. Sangren, ``Spectral theory of Dirac's radial relaltivistic wave equation,'' J. Math. Phys.3 882-890 (1962). ``Expansions associated with a pair of singular first-order differential equations,'' J. Math Phys. 4, 999-1008 (1963).

15
K. Kodaira, ``On ordinary differential equations of any even order and the corresponding eigenfunction expansions,'' Amer. J. Math. 72, 502-544 (1950).

16
W. N.Everitt, ``The Sturm-Liouville problem for fourth-order differential equations,'' Quart. J. Math 8 146-160 (1957); ``Fourth-order singular differential equations.'' Math. Ann. 149 320-340 (1963); ``On the limit-point classification of fourth-order differential equations,'' J. London Math. Soc. 44, 273-281 (1969).

17
K. Nikolsky, ``Das Ozillatorproblem nach der Diracschen Theorie,'' Z. Phys. 62 677-681 (1930).

18
I. Postepska, ``Harmonische Ozillator nach der Diracschen Wellengleichung.'' Acta. Phys. Pol. 4. 269-280 (1935).

19
G L. Sewell, ``An approximate relation between the energy levels of a particle in a field of a given potential energy, calculated on the relalivislic and non-relalivislic theories,'' Proc. Cambridge Phil. Soc. 45. 631-637 (1949).

20
E. C. Titchmarsh, ``On the relation between the eigenvalues in relativislic and non-relalivistic quantum mechanics,'' Proc. Roy. Soc. Ser. A 266, 33-46 (1962); Quart. J Math. 15, 193-207 (1964).



Microcomputadoras
2000-10-13