By Bernd Thaller
Advanced visible Quantum Mechanics is a scientific attempt to enquire and to educate quantum mechanics through computer-generated animations. it's a self-contained textbook that mixes chosen issues 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 ideas. a chain of appendices covers vital issues from perturbation and scattering conception. The booklet locations an emphasis on rules and ideas, with a good to average volume of mathematical rigor.
Though this ebook stands on my own, it could possibly even be paired with Thaller visible Quantum Mechanics to shape a complete 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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Additional info for Advanced Visual Quantum Mechanics
Like the radial equation, the eigenvalues E ;nr are independent of the quantum number m. 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.
85) At each point, the three unit vectors thus form a right-handed, orthonormal system. 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 .
5. 5. The Possible Eigenvalues of Angular-Momentum Operators In this section, we present a purely algebraic approach to the solution of the eigenvalue problem for the angular-momentum operators. For simplicity, we work with units where has the numerical value 1. 57) [J1 , J2 ] = iJ3 , [J2 , J3 ] = iJ1 , [J3 , J1 ] = iJ2 . A lot can be learned by studying these relations. Because of these relations, we cannot hope to ﬁnd simultaneous eigenvectors belonging to nonzero eigenvalues. Indeed, assume that ψ is a simultaneous eigenvector of, say, J1 and J2 .