Dr. Handy received all of his four degrees from Columbia University, concentrating in mathematics and physics, at the undergraduate level, and theoretical physics (i.e. path integral formulations of non-abelian gauge theories) at the graduate level, working under Dr. A. Mueller and Dr. John Klauder (AT&T). As a freshman he assisted Dr. Martin Gutzwiller (IBM) in his computational investigations of quantum chaos. He was the first participant and graduate of the AT&T Cooperative Research Fellowship Program which has produced many minority and women Ph.D's in diverse academic disciplines. From 1978 - 81 he was a postdoctoral fellow at the Los Alamos National Laboratory. Following a brief appointment in industry, Dr. Handy joined the faculty of (presently) Clark Atlanta University (1983 - 2005) where he co-founded the Center for Theoretical Studies of Physical Systems, one of the first successful HBCU-research and student mentoring centers in the nation. In 2005 he became the chair of the new physics program at Texas Southern University, in Houston, Texas. While at LANL, he focused on the development of singular perturbation, multi-scale, methods for strong coupling field theory problems. This led to a fascination with the Moment Problem (i.e. reconstruction of a positive signal through a hierarchy of, successively decreasing, scale related information) in pure mathematics and its incorporation into quantum physics. One branch of these investigations would eventually lead to the theory of Contiuous Wavelets as derived, through other means, by Grossman and Morlet. A second branch, funded through an NSF "Creativity Award" (1983 - 88), was the discovery that the moment problem leads to powerful new computational methods (within the spirit of control theory) for reliably predicting certain features of singular perturbation/strongly coupled systems. From 1985 - 1988 Dr. Handy pioneered these methods, together with D. Bessis. This approach, The "Eigenvalue Moment Method (EMM)", is now recognized as one of the first applications of Semidefinite Programming (SDP) in quantum physics, anticipating the importance of these methods by at least a decade. More recently, SDP has made a tremendous impact both in pure mathematics (i.e. combinatorics) and quantum chemistry through the N-Body problem reduction methods advocated by D. Mazziotti (U. Chicago), and others. Dr. Handy continues his research in this general area, with close to seventy publications, developing new ways of exploiting positivity constraints to computationally solve various quantum physics problems through the generation of rapidly converging lower and upper bounds to the physical parameters.

Ph. D. in Theoretical Physics
Columbia University, New York
May 1978

M. Ph.D.,Theoretical Physics
Columbia University, New York
May 1976

M. A., Physics
Columbia University, New York
May 1975

B. A., Physics, Minor in Mathematics
Columbia College, New York
May 1972

1. C. R. Handy, "Diagrammatics of Gauge Transformations for General Gauge Theories," Phys. Rev. D19, 585 (1979).

2. C. R. Handy, "Strong Coupling Singular Perturbation Theory and the Moments Problem," Phys. Rev. D 24, 378 (1981).

3. C. R. Handy, "Lattice Multiscale Singular Perturbation Theory," Proceedings of the International Conference on Differential Equations, edited by Ian W. Knowles and Roger T. Lewis, North Holland, 279 (1984).

4. C. R. Handy and S. P. Hirshman, "Accelerated Convergence of the Steepest Descent Method for Magnetohydrodynamic Equilibria," J. Comp. Physics 60, 338 (1985).

5. C. R. Handy, "Combining the Methods of Harmonic Balance and Kryloff-Bogoliuboff,"J. Sound and Vibration, 102, 243 (1985).

6. C. R. Handy, " Harmonic Balance Methods and the Theory of Generalized Pade Approximants," J. of Sound and Vibration, 102, 247 (1985).

7. C. R. Handy, "Multiple-Turning Point Problems and Lattice Multiscale Singular Perturbation," Phys. Rev. D. 3168 (1985).

8. C. R. Handy and D. Bessis, "Rapidly Convergent Lower Bounds for the Schrodinger Equation Ground State Energy," Phys. Rev. Lett. 55, 931 (1985).

9. C. R. Handy, "Hankel-Hadamard Analysis of Quantum Potential $x^2 + {{\lambda x^2} \ {1+gx^2}}$," J. Phys. A: Math. Gen. 18, 3593 (1985).

10. C. R. Handy, "Polya-Pade Fourier Resonance Reconstruction and Singular Perturbation Theory," J. of Nonlinear Analysis, Theory, Methods \& Applications, 10, 391 (1986).

11. D. Bessis and C. R. Handy, "Systematic Construction of Upper and Lower Bounds to the Ground State Energy of the Schrodinger Equation," International Journal of Quantum Chemistry: Quantum Chemistry Symposium 20, 21 (John Wiley \& Sons, INc. 1986).

12. D. Bessis, E. R. Vrscay, and C. R. Handy, "Hydrogenic Atoms in the External Potential $V(r) = g r + \lambda r^2$: Exact Solutions and Ground State Eigenvalue Bounds Using Moment Methods," J. Phys. A: Math. Gen. 20, 419 (1987).

13. C. R. Handy and R. M. Williams, "Rapid Wavefunction Reconstruction through Hankel-Hadamard Moments Analysis," J. Phys. A: Math. Gen. 20, 2315 (1987).

14. C. R. Handy, "Moment Method Quantization of a Linear Differential Eigenvalue Equation for $|\Psi|^2$," Phys. Rev. A 36, 4411 (1987).

15. C. R. Handy, "Nonnegativity and Moment Quantization for $|\Psi|^2$", Phys. Lett. A 124, 308 (1987).

16. C. R. Handy, "A Solution to the One-Dimensional Missing Moment Problem," J. Math. Phys. 29, 32 (1988).

17. C. R. Handy, D. Bessis, and R. M. Williams, "Moment Problem Formulation of the Simplified Ideal Magnetohydrodynamic Ballooning Equation," J. Math. Phys. 29, 717 (1988).

18. C. R. Handy, D. Bessis, and T. R. Morley, "Generating Quantum Energy Bounds by the Moment Method: A Linear Programming Approach," Phys. Rev. A 37, 4557 (1988).

19. C. R. Handy, D. Bessis, G. Sigismondi, and T. D. Morley, "Rapidly Converging Bounds for the Ground State Energy of Hydrogenic Atoms in Superstrong Magnetic Fields," Phys. Rev. Lett. 60, 253 (1988).

20. C. R. Handy, L. Luo, G. Mantica, and A. Z. Msezane, "Exact Bounds to One Dimensional Potential Scattering Amplitudes Through the Classical Theory of Moments," Phys. Rev. A 38, 490 (1988).

21. A. Z. Msezane, C. R. Handy, G. Mantica, and J. Lee, "Close Coupling Analysis of Electron Impact Excitation of Na(4s)," Phys. Rev. A 38, 1604 (1988).

22. C. R. Handy and J. Q. Pei, "Moment Method Analysis of the Ground State of Discretized Bosonic Systems," Phys. Rev. A 38, 3175 (1988).

23. C. R. Handy, "Positivity and the Quantization of Singular Strongly Coupled Physical Systems: An Operations Research Approach to Modern Physics," Proceedings of the First Edward Bouchet International Conference on Physics and Technology, Trieste, Italy (1988).

24. C. R. Handy, G. Mantica, and J. B. Gibbons, "Quantization of Lattice Schrodinger Operators via the Trigonometric Moment Problem," Phys. Rev. A 39, 3256 (1988).

25. E. R. Vrscay and C. R. Handy, "The Perturbed Two Dimensional Oscillator: Eigenvalues and Infinite Field Limits via Continued Fractions, Renormalized Perturbation Theory and Moment Method," J. Phys. A: Math. Gen. 22, 823 (1989).

26. C. R. Handy and D. Bessis, Response to Comments by Rech, Gallas, and Gallas, Phys. Rev. Lett. 62, 2199 (1989).

27. C. R. Handy and G. Mantica, "Inverse Problems in Fractal Construction: Moment Method Solution", Physica D 43, 17 (1990).

28. C. R. Handy and P. Lee, "Positivity and the Quantization of Physical Systems: The C-Shift Moment Method," J. Phys. A: Math. Gen. 24, 1565 (1991).

29. C. R. Handy, B. G. Giraud, and D. Bessis, "A Dynamical System Formulation of the Eigen-value Moment Method," Phys. Rev. A 44, 1505 (1991).

30. C. R. Handy and G. L. Ndow "Euclidean Time Formulation of the Eigenvalue Moment Method: A Moment Problem-Convexity Analysis of Barnsley's Theorem", J. of Phys. A: Math. and Gen. 25, 2669-2681 (1992).

31. C. R. Handy, "Application of the Eigenvalue Moment Method to the Quartic Anharmonic Double Well Oscillator", Phys. Rev. A 46, 1663 (1992).

32. C. R. Handy, "An Eigenvalue Moment Method Analysis of the $V(x) = {{\omega^2}\over 2} x^2 + \alpha x^3 + \beta x^4$ Anharmonic Oscillator," Molecular Physics,76, 1235 (1992).

33. C. R. Handy, H. Hayes, D. Stephens, J. Joshua, and S. Summerour "Application of the Eigenvalue Moment Method to Important One Dimensional Quantum Systems", J. Phys. A. 26, 2635 (1993).

34. C. R. Handy, K. Appiah, and D. Bessis "Moment-Problem Formulation of a Minimax Quantization Procedure", Phys. Rev. A 50, 988 (1994).

35. C. R. Handy, "Extension of a Moment Problem Mini-Max Quantization Procedure to Anharmonic Potentials", Phys. Rev. A 52, 3468 (1995).

36. C. R. Handy, J. Maweu, and L. Atterberry, "Variational Formulation of a Moment Problem Quantization Method", J. Math. Phys. 37, 1182 (1996).

37. C. R. Handy, "Ground-State Energy Bounds of Singular Potentials", Physics Letters A 216, 15 (1996).

38. C. R. Handy "A Moment Equation Reformulation of Rayleigh-Ritz Theory", J. Phys. A: Math. & Gen. 29, 4093 (1996).

39. C. R. Handy and R. Murenzi, "Continuous Wavelet Transform Analysis of One Dimensional Quantum Bound States from First Principles," Phys. Rev. A 54, 3754 (1996).

40. C. R. Handy and R. Murenzi, "Continuous Wavelet Transform Analysis of One Dimensional Quantum Ground States," CRM Proceedings and Lecture Notes: Spline Functions and the Theory of Wavelets, American Mathematical Society, Providence, Rhode Island, Eds. S. Dubuc and G. Deslauriers,(1999). (1996 Workshop, at the Centre de Recherches Mathematiques, University of Montreal, Quebec, Canada)

41. C. R. Handy and R. Murenzi, "Continuous Wavelet Transform Analysis of Quantum Systems with Rational Potentials," J. Phys. A 30, 4709 (1997).

42. C. J. Tymczak, G. S. Japaridze, C. R. Handy, and Xiao-Qian Wang, "New Perspective on Inner Product Quantization," Phys. Rev. Lett. 80, 3673 (1998).

43. C. J. Tymczak, G. S. Japaridze, C. R. Handy, and Xiao-Qian Wang, "Iterative Solutions to Quantum Mechanical Problems," Phys. Rev. A 58, 2708 (1998).

44. C. R. Handy and R. Murenzi, "Moment-Wavelet Quantization: A First Principles Analysis of Quantum Mechanics through continuous Wavelet Transform Theory," Phys. Lett. A 248, 7 (1998).

45. C. R. Handy and R. Murenzi, "On the Equivalence of Moment Quantization and Continous Wavelet Transform Analysis," J. Phys. A: Math. Gen. 31, 9897 (1998).

46. C. R. Handy and R. Murenzi, "Moment Quantization and (A-adic) Discrete Continuous Wavelet Transform Theory," J. Phys. A: Math. Gen. 32, 8111 (1999).

47. C. R. Handy and R. Murenzi, " Moment-Wavelet Quantization of Schrodinger Operators," Proceedings of the International Conference: Perspective in Mathematical Physics, Conference in the honor of Alexander Grossmann (Marseille- Luminy , July 28 - August 1, 1997 France). CPT-98/P.3748, CNRS-UPR 7061 - CPT, edited by M. Holschneider and G. Saracco.

48. C. R. Handy, R. Murenzi, K. Bouyoucef, and H. A. Brooks, "Moment-wavelet quantization and (complex) multiple turning point contributions," J. Phys. A: Math. Gen. 33, 2151 (2000).

49. C. R. Handy and H. A. Brooks "Scalets, Wavelets, and (Complex) Turning Point Quantization", J. Phys. A: Math. Gen. 34, 3577 (2001).

50. C. R. Handy, "New Perspectives in Moment-Wavelet Analysis from Quantum Operator Theory: Scalets and Local Quantization,'' Proceedings of the Council for African-American Researchers in the Mathematical Sciences, Contemporary Mathematics, Vol. 284, edited by G. M. N'Guerekata, (American Mathematical Society, Providence, R.I. (2001)).

51. C. R. Handy, "Turning Point Quantization and Scalet-Wavelet Analysis,'' Chapter 6 in Computational Chemistry: Review of Current Trends, Vol. 6 edited by J. Leszczynski (World Scientific, Singapore (2001)).

51. C. R. Handy, "Turning Point Quantization and Scalet-Wavelet Analysis,'' Chapter 6 in Computational Chemistry: Review of Current Trends, Vol. 6 edited by J. Leszczynski (World Scientific, Singapore (2001)).

52. C. R. Handy, "Generating Converging Eigenenergy Bounds for the Discrete States of the $-ix^3$ non-Hermitian Potential'', J. Phys. A: Math. Gen. 34, L271 (2001).

53. C. R. Handy and X. Q. Wang, "Extension of a Spectral Bounding Method to Complex Rotated Hamiltonians, with Application to $P^2-iX^3$,'' J. Phys. A: Math. Gen. 34, 8297 (2001).

54. C. R. Handy, "Generating Converging Bounds to the (Complex) Discrete States of the $P^2 + iX^3 + iaX$ Hamiltonian,'' J. Phys. A: Math. Gen. 34, 5065 (2001).

55. C. R. Handy, D. Khan, X. Q. Wang, and C. J. Tymczak, "Multiscale Reference Function Analysis of the PT Symmetry Breaking Solutions for the $P^2 + iX^3 + ia X$ Hamiltonian," J. Phys. A: Math. Gen. 34, 5593 (2001).

56. Z. Yan and C. R. Handy, "Extension of a Spectral Bounding Method to the PT-Invariant STates of the $-(iX)^N$ non-Hermitian Potential,'' J. Phys. A: Math. Gen. 34, 9907 (2001).

57. C. R. Handy and A. Z. Msezane, "Generation of Converging Regge-Pole Bounds: A New Formulation of Complex Rotation Quantization,'' J. Phys. A: Math. Gen. 34, L531 (2001).

58. C. R. Handy, C. Trallero-Giner, and A. H. Rodriguez, "Generating Bounds for the Discrete State Energy Values of the Infinite Quantum Lens Potential,'' J. Phys. A: Math. Gen. 34, 10991 (2001).

59. C. R. Handy, A. Z. Msezane, and Z. Yan, " Generation of Converging Regge Pole Bounds for Arbitrary Rational Fraction Scattering Potentials,'' J. Phys. A: Math. Gen. 35, 6359 (2002).

60. A. Rodriguez, C. R. Handy, and C. Trallero-Giner, "Excited States in the Infinite Quantum Lens Potential: Conformal Mapping and Moment Quantization Methods,'' J. Phys.: Condenced Matter 15, 8465 (2003).

61. C. R. Handy, C. J. Tymczak, and A. Z. Msezane, "High Precision Regge-Pole and Residues for Singular Scattering Potentials,'' Phys. Rev. A 66, 050701 (R) (2002).

62. C. R. Handy, D. Khan, S. Okbagabir, and T. Yarahmad " Moment Problem Quantization within A Generalized Scalet-Wigner (Auto-Scaling) Transform Representation,'' J. Phys. A: Math. Gen. 36, 1623 (2003).

63. C. R. Handy and X. Q. Wang, "Spectral Bounds for the PT-breaking Hamiltonian $p^2 + x^4 + iax$, J. Phys. A.: Math. & Gen. 36, 11513 (2003).

64. C. R. Handy "Positivity Representations for non-Hermitian Hamiltonians," Czechoslovak J. of Physics 54, 57 (2004).

65. A. Rodriguez, C. R. Handy, and C. Trallero-Giner, Reply to Comment on "Excited States in the Infinite Quantum Lens Potential: Conformal Mapping and Moment Quantization Methods,'' J. Phys.: Condenced Matter 16, 2945 (2004).

66. C. R. Handy "(Quasi)-convexification of Barta's (multi-extrema) bounding theorem", J. Phys. A: Math. Gen. 39, 3425 (2006)

• The Vocano Function #1
• The Vocano Function #2