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The stochastic mechanics of the ground-state of the hydrogen atom

Part of the Lecture Notes in Mathematics book series (LNM,volume 1158)

Keywords

  • Dirichlet Boundary Condition
  • Transition Density
  • Quantum Mechanical Probability
  • Forward Kolmogorov Equation
  • Hypergeometric Solution

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References

  1. A. Truman and J.T. Lewis: Stochastic Mechanics of the Bound States of the Hydrogen Atom, in course of preparation.

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  2. E.B. Davies: Quantum Stochastic Processes, Commun. Math. Phys. 15, 277–304 (1969).

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  3. N. Ikeda and S. Watanabe: Stochastic Differential Equations and Diffusion Processes. Amsterdam-Oxford-New York: North Holland 1981.

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  4. A. Friedman: Partial Differential Equations of Parabolic Type. Englewood Cliffs, New Jersey: Prentice Hall 1964.

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  5. E. Nelson, Dynamical Theories of Brownian Motion, Princeton: Princeton University Press 1967.

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  6. B. Simon: Semiclassical Analysis of Low-Lying Eigenvalues, II, Cal. Tech. Preprint 1984.

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  7. I. Davies and A. Truman: Laplace Asymptotic Expansions of Conditional Wiener Integrals and Generalized Mehler Kernel Formulae for Hamiltonians on L2 (ℛn), J. Phys. A17, 2773–2789 (1984).

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  8. S. Albeverio and R. Høegh-Krohn: A Remark on the Connection Between Stochastic Mechanics and the Heat Equation, J. Math. Phys. 15, 1745–1747 (1974).

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  9. H.P. McKean: Stochastic Integrals. Academic Press, New York (1969).

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© 1986 Springer-Verlag

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Truman, A., Lewis, J.T. (1986). The stochastic mechanics of the ground-state of the hydrogen atom. In: Albeverio, S.A., Blanchard, P., Streit, L. (eds) Stochastic Processes — Mathematics and Physics. Lecture Notes in Mathematics, vol 1158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080216

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  • DOI: https://doi.org/10.1007/BFb0080216

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15998-8

  • Online ISBN: 978-3-540-39703-8

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