Download PDF by Bernd Thaller: Advanced visual quantum mechanics

By Bernd Thaller

ISBN-10: 0387207775

ISBN-13: 9780387207773

 Visual Quantum Mechanics is a scientific attempt to enquire and to coach quantum mechanics via computer-generated animations. even though it is self-contained, this booklet is a part of a two-volume set on visible Quantum Mechanics. the 1st ebook seemed in 2000, and earned the ecu educational software program Award in 2001 for oustanding innovation in its box. whereas subject matters in booklet One in most cases involved quantum mechanics in a single- and two-dimensions, publication units out to provide third-dimensional structures, the hydrogen atom, debris with spin, and relativistic particles. It additionally includes a easy direction on quantum details thought, introducing subject matters like quantum teleportation, the EPR paradox, and quantum desktops. jointly the 2 volumes represent a whole path in quantum mechanics that areas an emphasis on principles and ideas, with a good to average volume of mathematical rigor. The reader is predicted to be acquainted with calculus and common linear algebra. from now on mathematical suggestions may be illustrated within the textual content.

Th CD-ROM contains a huge variety of Quick-Time video clips provided in a multimedia-like surroundings. the films illustrate and upload colour to the text, and permit the reader to view time-dependent examples with a degree of interactivity. The point-and-click interface is not any tougher than utilizing the web.

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Hence, im2 − m1 = 0, and because the eigenvalues of symmetric operators are always real, this implies that m1 = m2 = 0. We conclude that there are no nontrivial simultaneous eigenvectors belonging to nonzero eigenvalues. 58) J 2 = J12 + J22 + J32 commutes with all components Jk , [J 2 , Jk ] = 0, for k = 1, 2, 3. 59) Hence, we could try to find simultaneous eigenvectors for the operator J 2 and any one of the components, say J3 . We are going to prove the following theorem. 1. Assume that there is a simultaneous eigenvector of the commuting operators J 2 and J3 .

8. 12. Classical versus quantum position probability densities as functions of the polar angle ϑ for the rigid rotator. The quantum probability (filled curve) oscillates around the classical probability (black line). The quantum wave function decreases rapidly outside the classically allowed region whose borders are indicated by the vertical gray lines. 12 compares the quantum and classical probability densities as functions of ϑ. 8 depict the relations between the classically allowed region of the rigid rotator, the classical ϑ-oscillation, and the quantum probability density as a function of ϑ.

140) ϑ(t) + sin ϑ(t) ϕ(t) 2 If there are no external forces, the kinetic energy is a constant of motion. Another conserved quantity is the angular momentum. In fact, one finds that the above expression for the kinetic energy is just T = L2 /2. In spherical coordinates, we obtain a particularly simple expression for the third component of the angular momentum, L3 (t) = x1 (t) x˙ 2 (t) − x˙ 1 (t) x2 (t) = sin ϑ(t) 2 ϕ(t). 141) Denoting the constant value of L3 by m, we may eliminate the angular velocity ϕ˙ and express the kinetic energy solely in terms of ϑ T = m2 1 ˙ 2 ϑ(t) + .

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Advanced visual quantum mechanics by Bernd Thaller

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