By Darwin C. G.

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**Additional resources for A Quantum Theory of Optical Dispersion**

**Sample text**

In a similar manner we obtain (13) with (20) «i" = n n E x~(*K(«)> where X {X) ~ \1 if a: >-*(*). Then (14) is immediate from (18) and (20). 1 Quantum Central Limit Theorem CCR-Algebra as a Quantum Probability Space We denote by T(C) the one-mode Boson Fock space. For k = 0,1,2, • • • let \P(fc) be the number vector defined in a usual manner. Then {\P(k)} becomes a complete orthonormal basis of T(C) = J2T=o ^^V(k). The annihilation and creation operators are defined by B-V(k) = VkV(k-l), B - tf(0) = 0, k>\, and £+*(£) = Vfc + ltf(Jfe + l), k > 0, respectively.

J. 20 (1990) 137-157 Quantum Information III, pp. 35-43 Eds. T. Hida and K. Saito © 2001 World Scientific Publishing Company 35 TUNNELING EFFECT BASED ON THE NELSON'S Q U A N T U M STOCHASTIC PROCESS APPROACH COMPARISON WITH A N E U T R O N SPIN ECHO EXPERIMENT TAKAAKI HASHIMOTO AND TAKEO TOMOMURA Department of Applied Physics Faculty of Engineering, Fukui University Bunkyo 3-9-1, Fukui 910-8507, JAPAN The determination of the tunneling time associated with the passage of a particle through a tunnel barrier has been a long standing problem.

We can see that < Tr > is much larger than < Tp > and the effect of the 'hesitation' is not negligible. When the transmissivity becomes larger, < Tr > becomes larger but < Tv > becomes smaller. They show the opposite tendency. The residence time has the same tendency with the Larmor time, but the value is much larger. 42 Figure 8: The time dependence of the drift velocity r miumisao Figure 9: Refraction and reflection of the neutron beam 5 Discussion We expected that the residence time corresponds to the Larmor time as a particle with magnetic moment makes precession only in the magnetic tunneling barrier.

### A Quantum Theory of Optical Dispersion by Darwin C. G.

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