Advanced visual quantum mechanics by Bernd Thaller

By Bernd Thaller

 Visual Quantum Mechanics is a scientific attempt to enquire and to coach quantum mechanics because of 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 publication seemed in 2000, and earned the ecu educational software program Award in 2001 for oustanding innovation in its box. whereas subject matters in ebook One frequently involved quantum mechanics in a single- and two-dimensions, e-book units out to give third-dimensional structures, the hydrogen atom, debris with spin, and relativistic particles. It additionally encompasses a easy path on quantum info thought, introducing subject matters like quantum teleportation, the EPR paradox, and quantum desktops. jointly the 2 volumes represent an entire path in quantum mechanics that locations an emphasis on rules and ideas, with a good to average volume of mathematical rigor. The reader is anticipated to be conversant in calculus and simple linear algebra. to any extent further mathematical options should be illustrated within the textual content.

Th CD-ROM contains a huge variety of Quick-Time videos offered in a multimedia-like surroundings. the flicks 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 net.

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190) is in the domain of the self-adjoint operator H. The mathematical theory tells us that these functions have to be bounded and continuous on R3 , at least for physically meaningful (that is, not too singular) potential functions V . Therefore, (1/r) f ;nr (r) has to remain bounded, as r → 0. 188). It is distinguished by the boundary condition u(r) → 0, as r → 0. The solution u(E, r) turns out to be square-integrable only for exceptional values of the parameter E, that is, for the eigenvalues E = E ;nr .

The number nr is called the radial quantum number. It just serves as a label for the different eigenvalues of the radial equation. We denote the radial eigenfunction belonging to the eigenvalue E ;nr by f ;nr (r). 10. 190) where (r, ϑ, ϕ) are the spherical coordinates of x, and m is any of the eigenvalues of L3 . The functions ψ ,m;nr are simultaneous eigenstates of H, L2 , and L3 , belonging to the eigenvalues E ;nr , ( + 1), and m, respectively. For every possible energy E ;nr and every possible we have 2 + 1 linearly independent eigenfunctions ψ ,m;nr , with m = − , − + 1, .

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. 2. Special topic: Curvilinear coordinates It is worthwhile to consider the transition from classical to quantum mechanics for the rigid rotator in more detail. The classical kinetic energy of a particle with mass m = 1 is given by T (t) = 1 2 3 x˙ i (t)2 .

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