By Bernd Thaller

Visual Quantum Mechanics is a scientific attempt to enquire and to coach quantum mechanics as a result of 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 e-book seemed in 2000, and earned the eu educational software program Award in 2001 for oustanding innovation in its box. whereas subject matters in publication One as a rule involved quantum mechanics in a single- and two-dimensions, ebook units out to give three-d structures, the hydrogen atom, debris with spin, and relativistic particles. It additionally features a uncomplicated path on quantum info idea, introducing issues like quantum teleportation, the EPR paradox, and quantum desktops. jointly the 2 volumes represent a whole direction in quantum mechanics that locations an emphasis on principles and ideas, with a good to reasonable quantity of mathematical rigor. The reader is anticipated to be acquainted with calculus and ordinary linear algebra. to any extent further mathematical innovations might be illustrated within the textual content.

Th CD-ROM incorporates a huge variety of Quick-Time videos provided in a multimedia-like setting. the flicks 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 more challenging than utilizing the web.

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The action of the free time evolution exp(−iL on a sphere will be discussed next. 4. Dynamics of the rigid rotator The time evolution of an eigenfunction of the rigid rotator Hamiltonian is rather trivial. 125) is a solution of the time-dependent Schr¨ odinger equation. The ground state of the rigid rotator has energy E0 = 0, and hence the corresponding wave function does not depend on time at all. 7. PARTICLE ON A SPHERE 37 The fact that the Schr¨ odinger equation is linear means that we can consider linear combinations of eigenfunctions.

7. The absolute value |L| = L2 of the angular ( + 1), with being momentum can only take the values a non-negative integer. For a given , the component of the angular momentum in an arbitrary direction (here taken as the vertical direction) is also quantized and can only have the values − , − ( + 1), . . + . In a classical picture, the angular momentum vector (if measured with respect to a certain direction) thus lies on certain cones. Eigenvalues of the orbital angular momentum: The eigenvalues of the operator L2 are precisely the numbers 2 ( + 1), where is a non-negative integer.

114) E = mv 2 = m(rω)2 = Iω 2 , 2 2 2 where we have introduced the angular speed ω = v/r and the moment of inertia I = mr2 . 115) The angular momentum of a particle moving with velocity v on a sphere of radius r is L = mvr, or v = L/mr. Insert this into the expression for the energy to obtain L2 L2 = E= . 3 are all visualizations of the classical motion at a ﬁxed distance from the coordinate origin. 4It is general custom to denote the mass of the particle and the eigenvalue of L by 3 the same letter.