Quantum Mechanical Operators

  • George H. Duffey
Part of the Fundamental Theories of Physics book series (FTPH, volume 2)


Insofar as one can tell, a submicroscopic particle does not move along a definite path through the imposed Euclidean space. Instead, there exists a potentiality in each volume element; at a given time, the particle may appear in an infinitesimal region d3 r with the probability

ρd3 r = Ψd3 r.


Harmonic Oscillator Pure State State Function Eigenvalue Equation Hamiltonian Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Fong, P.: 1962, Elementary Quantum Mechanics, Addison-Wesley, Reading, Mass., pp. 297–360zbMATHGoogle Scholar
  2. Matthews, P. T.: 1963, Introduction to Quantum Mechanics, McGraw-Hill, New York, pp. 12 – 35zbMATHGoogle Scholar
  3. Rojansky, V.: 1942, Introductory Quantum Mechanics, Prentice-Hall, New York, pp. 1–42Google Scholar


  1. Borneas, M.: 1972, ‘A Quantum Equation of Motion with Higher Derivatives’, Am. J. Phys. 40, 248–251ADSCrossRefGoogle Scholar
  2. Das, R., and Sannigrahi, A. B.: 1981, ‘The Factorization Method and Its Applications in Quantum Chemistry’, J. Chem. Educ. 58, 383–388CrossRefGoogle Scholar
  3. David, C. W.: 1966, ‘Ladder Operator Solution for the Hydrogen Atom Electronic Energy Levels’, Am. J. Phys. 34, 984–985ADSCrossRefGoogle Scholar
  4. Dean, C. E., and Fulling, S. A.: 1982, ‘Continuum Eigenfunction Expansions and Resonances: A Simple Model’, Am. J. Phys. 50,540–544.MathSciNetADSCrossRefGoogle Scholar
  5. Edwards, I. K.: 1979, ‘Quantization of Inequivalent Classical Hamiltonians’, Am. J. Phys. 47, 153–155.ADSCrossRefGoogle Scholar
  6. Flores, J., Henestroza, E., Mello, P. A., and Moshinsky, M.:. 1981, ‘Decay of a Compound Particle and the Einstein-Podolsky-Rosen Argument’, Am. J. Phys. 49,59–63.MathSciNetADSCrossRefGoogle Scholar
  7. Gruber, G. R.: 1976, ‘On the Transition from Classical to Quantum Mechanics in Generalized Coordinates’, Found. Phys.6, 111–113.MathSciNetADSCrossRefGoogle Scholar
  8. Jordan, T. F.: 1975, ‘Why -i∇ is the Momentum’, Am. J. Phys. 43,1089–1093.ADSCrossRefGoogle Scholar
  9. Jordan, T. F.; 1976, ‘Conditions on Wave Functions Derived from Operator Domains’, Am. J. Phys. 44,567–570.ADSCrossRefGoogle Scholar
  10. Leaf, B.: 1979, ‘Momentum Operators for Curvilinear Coordinate Systems’, Am. J. Phys. 47, 811–813.ADSCrossRefGoogle Scholar
  11. Liboff, R. L., Nebenzahl, I., and Fleischmann, H. H.: 1973, ‘On the Radial Momentum Operator’, Am. J. Phys. 41,976–980.ADSCrossRefGoogle Scholar
  12. Mucci, J. F., and Haskins, P. J.: 1973, ‘Error Limits of Expectation Values in Quantum Mechanical Calculations’, Am. J. Phys. 41,987–989.ADSCrossRefGoogle Scholar
  13. Newmarch, J. D., and Golding, R. M.: 1978, ‘Ladder Operators for Some Spherically Symmetric Potentials in Quantum Mechanics’, Am. J. Phys. 46,658–660.ADSCrossRefGoogle Scholar
  14. Peña, de la, L., and Montemayor, R.: 1980, ‘Raising and Lowering Operators and Spectral Structure: A Concise Algebraic Technique’, Am. J. Phys. 48,855–860.ADSCrossRefGoogle Scholar
  15. Salsburg, Z. W.: 1965, ‘Factorization of the Radial Equation for the Hydrogen Atom’, Am. J. Phys. 33, 36–39ADSCrossRefGoogle Scholar
  16. Shoemaker, D. P.: 1972, ‘The Dirac Delta Function and the Density of States of Several Systems’, Chem Educ. 49, 607–610CrossRefGoogle Scholar
  17. Swenson, R. J., and Hermanson, J. C.: 1972, ‘Energy Quantization and the Simple Harmonic Oscillator’, Am. J. Phys. 40, 1258–1260ADSCrossRefGoogle Scholar
  18. Villasenor-Gonzales, P., and Cisneros-Parra, J.: 1981, ‘Quantum Operators in Generalized Coordinates’, Am. J. Phys. 49,754–756.ADSCrossRefGoogle Scholar
  19. Winter, R. G.: 1977, ‘Construction of Some Soluble Quantal Problems’, Am. J. Phys. 45, 569–571.ADSCrossRefGoogle Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1984

Authors and Affiliations

  • George H. Duffey
    • 1
  1. 1.Department of PhysicsSouth Dakota State UniversityUSA

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