By Ángel S. Sanz
Trajectory-based formalisms are an intuitively beautiful manner of describing quantum procedures simply because they permit using "classical" innovations. starting as an introductory point appropriate for college students, this two-volume monograph provides (1) the basics and (2) the functions of the trajectory description of simple quantum procedures. This moment quantity is focussed on basic and uncomplicated functions of quantum procedures equivalent to interference and diffraction of wave packets, tunneling, diffusion and bound-state and scattering difficulties. The corresponding research is performed in the Bohmian framework. by means of stressing its interpretational elements, the ebook leads the reader to another and complementary strategy to larger comprehend the underlying quantum dynamics.
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Additional info for A Trajectory Description of Quantum Processes. II. Applications: A Bohmian Perspective (Lecture Notes in Physics)
3 for the probability density. To better understand the quantum potential dynamics, let us proceed as follows. , Ψ (x, z, t) = ψx (x, t)ψz (z, t), and therefore Q is also expressible as a sum of two components all the way through, Q(x, z, t) = Qx (x, t) + Qz (z, t). 36) 16 1 Wave-Packet Dynamics: The Free-Particle Physics Fig. 1 µm). Each frame corresponds to each snapshot of the quantum potential displayed in Fig. 3 (labels have the same meaning). , Qz displays the form of an inverted parabola that widens as t increases.
36) 16 1 Wave-Packet Dynamics: The Free-Particle Physics Fig. 1 µm). Each frame corresponds to each snapshot of the quantum potential displayed in Fig. 3 (labels have the same meaning). , Qz displays the form of an inverted parabola that widens as t increases. 4 Quantum Diffraction 17 Fig. 7 Quantum potential ruling the dynamics of the Bohmian trajectories displayed in Fig. 5(a). 37) will remain essentially constant. , Qx essentially consists of two δ-functions at the borders of the slit and a plateau in between, as seen in Fig.
2mσ02 2n x(0). 40) As expected, the two first terms in the right-hand side of this expression are exactly the same that one would expect from a classical trajectory; note that the first term arises precisely when there is no spreading. However, the presence of the dependent (third) term makes that a divergence with respect to the classical motion is observable: it leads to a hyperbolic spreading of the trajectories. This is a very remarkable effect where the nonlocality, as defined above, plays an important role; in order to avoid crossing among trajectories, those with the outmost initial conditions (with respect to x0 = 0) will spread at a faster rate than the innermost ones.