The Operator Formulation of Classical Mechanics and Semiclassical Limit

@article{Prvanovic1999TheOF,
  title={The Operator Formulation of Classical Mechanics and Semiclassical Limit},
  author={Slobodan Prvanovic},
  journal={International Journal of Theoretical Physics},
  year={1999},
  volume={51},
  pages={1838-1846}
}
  • S. Prvanovic
  • Published 8 November 1999
  • Physics, Mathematics
  • International Journal of Theoretical Physics
The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing h0. For the later of these two extreme values, introduced operator algebra becomes equivalent to the algebra of observables of quantum mechanical system defined in the standard manner by operators in the Hilbert space. For the vanishing Planck constant, the… 
1 Citations
Problem of Measurement Within the Operator Formulation of Hybrid Systems
The basic concepts of classical mechanics are given in operator form. Then ahybrid systems approach with the operator formulation of both quantum andclassical sectors is applied to the case of an

References

SHOWING 1-10 OF 46 REFERENCES
Lie group dynamical formalism and the relation between quantum mechanics and classical mechanics
General structural features of dynamical theories can be exhibited in relations between classical and quantum mechanics; the essential structure is a Lie algebra of basic dynamical-variable fanctions
Quantum mechanics as a classical theory.
  • Heslot
  • Physics, Medicine
    Physical review. D, Particles and fields
  • 1985
TLDR
Basic features of quantum mechanics follow, such as the identification of observables with self-adjoint operators, and canonical quantization rules, which gives a new insight on the geometry of quantum theory.
Calculus for functions of noncommuting operators and general phase-space methods in quantum mechanics. II. Quantum mechanics in phase space
In Paper I of this investigation a new calculus for functions of noncommuting operators was developed, based on the notion of mapping of operators onto c-number functions. With the help of this
Operator Formulation of Classical Mechanics.
An operator formulation of classical mechanics is given. Rather than being concerned with Lie algebraic or abstract Hilbert space properties of classical mechanics, the present formulation is
Calculus for Functions of Noncommuting Operators and General Phase-Space Methods in Quantum Mechanics. III. A Generalized Wick Theorem and Multitime Mapping
The new c-number calculus for functions of noncommuting operators, developed in Paper I and employed in Paper II to formulate a general phase-space description of boson systems, deals with situations
CALCULUS FOR FUNCTIONS OF NONCOMMUTING OPERATORS AND GENERAL PHASE-SPACE METHODS IN QUANTUM MECHANICS. I. MAPPING THEOREMS AND ORDERING OF FUNCTIONS OF NONCOMMUTING OPERATORS.
A new calculus for functions of noncommuting operators is developed, based on the notion of mapping of functions of operators onto $c$-number functions. The class of linear mappings, each member of
Unique Hamiltonian Operators via Feynman Path Integrals
The old problem of how to represent uniquely a prescribed classical Hamiltonian H as a well‐defined quantal operator Ĥ is shown to have a clear answer within Feynman's path‐integral scheme (as
COMPLEX COORDINATES AND QUANTUM MECHANICS
By introducing complex canonical coordinates, classical and quantum mechanics may be embedded in the same formulation. In such a way, the connection between Poisson brackets and commutators,
Generalized Phase-Space Distribution Functions
A set of quasi-probability distribution functions which give the correct quantum mechanical marginal distributions of position and momentum is studied. The phase-space distribution does not have to
Semiclassical and Quantum Descriptions
In the semiclassical descriptions, it is usual to describe a quantum‐mechanical system in a classical language with (i) a correspondence between classical functions and operators of quantum mechanics
...
1
2
3
4
5
...