Advanced visual quantum mechanics by Bernd Thaller

By Bernd Thaller

 Visual Quantum Mechanics is a scientific attempt to enquire and to educate quantum mechanics by using 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 eu educational software program Award in 2001 for oustanding innovation in its box. whereas issues in publication One generally involved quantum mechanics in a single- and two-dimensions, ebook units out to give 3-dimensional platforms, the hydrogen atom, debris with spin, and relativistic particles. It additionally features a simple direction on quantum details idea, introducing issues like quantum teleportation, the EPR paradox, and quantum pcs. jointly the 2 volumes represent an entire direction in quantum mechanics that locations an emphasis on principles and ideas, with a good to reasonable volume of mathematical rigor. The reader is predicted to be accustomed to calculus and hassle-free linear algebra. from now on mathematical recommendations can be illustrated within the textual content.

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

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91) for the angular momentum in spherical coordinates, we arrive at ˆ = 1 L ˆ 2. 121) 2 2m r 2I 36 1. SPHERICAL SYMMETRY ˆ 2 has a discrete spectrum of eigenvalues, therefore the same The operator L is true for the energy of the rotator. Eigenvalues of the rigid rotator: A particle with mass m on a sphere with radius r can only have the energies 2 E = ( + 1), = 0, 1, 2, 3, . . 123) ψ ,m (ϑ, ϕ) = Y m (ϑ, ϕ), m = − , − + 1, . . , . 109) that ψ Sr2 ,m (ϑ, ϕ) 2 2 r sin ϑ dϑ dϕ = 1. 123) thus guarantees that the eigenfunctions are normalized on the sphere with radius r.

2, we stated that the rigid rotator is an approximate model for a diatomic molecule in a vibrational ground state. Here, we are going to refine the model and take into account the vibrational degree of freedom. We assume that the two atoms are bound together as a result of some complicated interaction between the two nuclei and all their electrons. The configuration with the minimal potential energy will have the two nuclei at some distance r0 from each other. The effective force between the nuclei would be repulsive at closer distances r < r0 and attractive at larger distances r > r0 .

166) From this, we conclude that the functions 2 +1 P (x) 2 form an orthonormal basis in the Hilbert space L2 ([−1, 1]). For any wave number k, the plane wave can be rewritten as f (x) = eik·x = eikr cos α = eikrx , with x = cos α ∈ [−1, 1]. 168) α is the angle between the vectors k and x. As a function of x (for fixed k and r), the function exp(ikrx) belongs to the Hilbert space L2 ([−1, 1]). Hence, it can be expanded in the Legendre polynomials in the usual way, 1 eikrx = c (kr) f (x), f (x) eikrx dx.

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