Abstract
The characteristic solutions of the Hamilton-Jacobi equation give the energies of conservative physical systems as functions of position and time. It is shown that these expressions are useful in the formation of probability densities in configuration space for canonical ensembles. Applications are given and discussed.
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References
Courant, R., and Hilbert, D. (1962).Methods in Mathematical Physics, Vol. II, Interscience, New York.
Feynman, R. P., and Hibbs, A. R. (1965).Quantum Mechanics and Path Integrals, McGraw-Hill, New York.
John, F. (1978).Partial Differential Equations, 3rd ed., Springer, New York.
Landau, L., and Lifchitz, E. (1966).Mécanique, Mir, Moscow.
Papoulis, A. (1965).Probability Random Variables and Stochastic Processes, McGraw-Hill, New York.
Schrödinger, E. (1967).Statistical Thermodynamics, Cambridge University Press, Cambridge.
Tolman, R. C. (1967).The Principles of Statistical Mechanics, Oxford University Press, Oxford.
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Ioannidou, H. Probability densities in configuration space and the Hamilton-Jacobi equation. Int J Theor Phys 34, 51–62 (1995). https://doi.org/10.1007/BF00670987
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DOI: https://doi.org/10.1007/BF00670987