Download PDF by Bernd Thaller: Advanced Visual Quantum Mechanics

By Bernd Thaller

ISBN-10: 0387207775

ISBN-13: 9780387207773

ISBN-10: 0387271279

ISBN-13: 9780387271279

Advanced visible Quantum Mechanics is a scientific attempt to enquire and to coach quantum mechanics because of computer-generated animations. it's a self-contained textbook that mixes chosen subject matters from atomic physics (spherical symmetry, the hydrogen atom, and debris with spin) with an creation to quantum info concept (qubits, EPR paradox, teleportation, quantum computers). It explores relativistic quantum mechanics and the unusual habit of Dirac equation strategies. a sequence of appendices covers very important issues from perturbation and scattering concept. The ebook areas an emphasis on principles and ideas, with a good to average quantity of mathematical rigor.
Though this ebook stands by myself, it will probably even be paired with Thaller visible Quantum Mechanics to shape a entire path in quantum mechanics. The software program for the 1st booklet earned the eu educational software program Award 2000 for awesome innovation in its box.

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Example text

We are going to discuss a very simple model that nevertheless shows many essential features of diatomic molecules. This potential is called Kratzer’s molecular potential (see Fig. 13). 197) where r is the internuclear distance. This function is spherically symmetric, and it has a minimum for r = r0 , with V (r0 ) = V0 . It is clear that this model is very unphysical both at very small distances and at very large distances. At small distances, the model potential describes a very strong repulsive potential with a 1/r2 -singularity (too strong for the Coulomb repulsion of the positively charged nuclei which is proportional to 1/r).

86) 28 1. SPHERICAL SYMMETRY The collection of formulas is completed by giving the expression for the gradient operator ∇ in spherical coordinates ˆ = er ∂ + 1 ∇ ∂r r eϑ ∂ 1 ∂ + eϕ ∂ϑ sin ϑ ∂ϕ . 87) This formula has to be understood as follows. The gradient of a function can either be evaluated in Cartesian coordinates or in spherical coordinates. 86). The spherical coordinate space is a three-dimensional space where the coordinate axes describe the r-, ϑ-, and ϕ-coordinates of a point in R3 . 6 visualizes the familiar examples of linear and circular motion, which look rather unfamiliar in the spherical coordinate space.

We conclude that the eigenfunctions form an orthonormal basis in the Hilbert space L2 (Sr2 ) of square integrable functions on the sphere of radius r. 150) below). For a particle constrained to the surface ˆ 2 plays the same role as the operator − 2 ∆ for of a sphere, the operator L a particle in R3 : It is proportional to the kinetic energy and it generates ˆ 2 / 2 is the so-called Laplace-Beltrami the free time evolution. ) The action of the free time evolution exp(−iL on a sphere will be discussed next.

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Advanced Visual Quantum Mechanics by Bernd Thaller


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