By Bernd Thaller

ISBN-10: 0387207775

ISBN-13: 9780387207773

Visual Quantum Mechanics is a scientific attempt to enquire and to coach quantum mechanics using computer-generated animations. even though it is self-contained, this ebook is a part of a two-volume set on visible Quantum Mechanics. the 1st booklet seemed in 2000, and earned the ecu educational software program Award in 2001 for oustanding innovation in its box. whereas issues in booklet One more often than not involved quantum mechanics in a single- and two-dimensions, ebook units out to offer three-d platforms, the hydrogen atom, debris with spin, and relativistic particles. It additionally incorporates a uncomplicated path on quantum details concept, introducing themes like quantum teleportation, the EPR paradox, and quantum desktops. jointly the 2 volumes represent an entire direction in quantum mechanics that locations an emphasis on principles and ideas, with a good to average quantity of mathematical rigor. The reader is anticipated to be accustomed to calculus and hassle-free linear algebra. to any extent further mathematical options should be illustrated within the textual content.

Th CD-ROM encompasses a huge variety of Quick-Time videos offered in a multimedia-like atmosphere. 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 more challenging than utilizing the net.

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**Extra resources for Advanced visual quantum mechanics**

**Example text**

X + iy x2 + y2 m Pm z . 112) For example, 1 Y00 = √ , 4π Y10 = 3 z , 4π r Y1±1 = ∓ 3 x ± iy . 7. 1. Classical particle on a sphere Here, we consider a quantum mechanical system that is only able to perform a rotational motion. Imagine a particle with mass4 m whose motion is restricted to the surface of a sphere. There are no other forces. This particle has two degrees of freedom, its position on the sphere is given by two angular coordinates, the longitude and the latitude, described by the angles ϑ and ϕ.

109), we can perform the integration over the angles ϑ and ϕ. This removes the sum and m , because only the term with = and m = m gives a over contribution. 9. FREE SCHRODINGER EQUATION IN SPHERICAL COORDINATES 49 where (k, ϑ , ϕ ) are the spherical coordinates of k ∈ R3 . We have found that ˆ the Fourier transform ψ(k) is again an eigenfunction of L2 and L3 with the same quantum numbers and m. The Fourier transform maps an angular momentum eigenspace into itself. The function h is connected to f via an integral transformation that is known as the Hankel transformation, 2 π h(k) = (−i) ∞ 1/2 f (r) jˆ (kr) dr.

163) h jˆ (z) = Further details about the Riccati-Bessel functions can be found in the book [1], where the notation jˆ(z) = zj(z), and n ˆ (z) = zy(z) is used. 3. Special Topic: Expanding the plane wave The plane waves exp(ik·x) are important solutions of the free-particle Schr¨ odinger equation, despite the fact that they are not square-integrable. 153). The radial part of a plane wave in the subspace with angular-momentum quantum number is just the Riccati-Bessel function jˆ (kr). This result is important for the applications to stationary scattering theory with spherically symmetric potentials.

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