By Bernd Thaller
Advanced visible Quantum Mechanics is a scientific attempt to enquire and to educate quantum mechanics because of computer-generated animations. it's a self-contained textbook that mixes chosen themes from atomic physics (spherical symmetry, the hydrogen atom, and debris with spin) with an creation to quantum details conception (qubits, EPR paradox, teleportation, quantum computers). It explores relativistic quantum mechanics and the unusual habit of Dirac equation suggestions. a sequence of appendices covers vital issues from perturbation and scattering idea. The publication areas an emphasis on rules and ideas, with a good to average quantity of mathematical rigor.
Though this booklet stands on my own, it may even be paired with Thaller visible Quantum Mechanics to shape a entire direction in quantum mechanics. The software program for the 1st e-book earned the eu educational software program Award 2000 for extraordinary innovation in its box.
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Extra resources for Advanced Visual Quantum Mechanics
4. 175) ψ(x) = f (r) Y m (ϑ, ϕ), r where (r, ϑ, ϕ) are the spherical coordinates of the point x ∈ R3 . Obviously, ψ is an eigenfunction of the angular-momentum operators L2 and L3 . We ˆ want to ﬁnd the Fourier transform ψ(k). 174)), e −ik·x 4π = kr ∞ (−i) jˆ (kr) Y m (ϑ , ϕ ) Y m (ϑ, ϕ). 178) =0 m =− Using the orthonormality of the spherical harmonics, Eq. 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.
128) ,m with c ,m = S2 Y m (ϑ, ϕ) ψ0 (ϑ, ϕ) dΩ. 129) The time evolution of the wave function is periodic in time, ψ(t + T, ϑ, ϕ) = ψ(t, ϑ, ϕ) with period T = 2π. 12 is a collection of several movies showing various time-dependent states of the rigid rotator. 13 visualizes the time evolution of initially well-localized (Gaussian) states. 14, the initial state has roughly the shape of the letter Ψ. This illustrates that we can indeed compute the time evolution of any square-integrable initial function on the sphere.
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. A classical particle subject to these constraints will move along the geodesics of the sphere (great circles) with constant (angular) velocity.