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Unformatted text preview: Lecture 16, p 1 It was almost as incredible as if you fired a 15inch shell at a piece of tissue paper, and it came back to hit you!E. Rutherford (on the discovery of the nucleus) Lecture 16, p 2 Special (Optional) Lecture Quantum Information c One of the most modern applications of QM c quantum computing c quantum communication cryptography, teleportation c quantum metrology c Prof. Kwiat will give a special 214level lecture on this topic c Sunday, Feb. 27 c 3 pm, 151 Loomis c Attendance is optional, but encouraged. Lecture 16, p 3 Lecture 16: 3D Potentials and the Hydrogen Atom P(r) 4a 1 r r = a z x L L L ( 29 2 2 2 2 2 8 z y x n n n n n n mL h E z y x + + = ) ( ) ( ) ( ) , , ( z y x z y x = o a / r 3 o e a 1 ) r ( = 2 6 13 n eV . E n = Lecture 16, p 4 Final Exam: Monday, March 7 Homework 6: Due Saturday (March 5), 8 am Up to now: General properties and equations of quantum mechanics Timeindependent Schrodingers Equation (SEQ) and eigenstates. Timedependent SEQ, superposition of eigenstates, time dependence. Collapse of the wave function, Schrodingers cat Tunneling This week: 3 dimensions, angular momentum, electron spin, H atom Exclusion principle, periodic table of atoms Next week: Molecules and solids, consequences of Q. M. Metals, insulators, semiconductors, superconductors, lasers, . . Overview of the Course Lecture 16, p 5 Today 3Dimensional Potential Well: Product Wave Functions Degeneracy Schrdingers Equation for the Hydrogen Atom: Semiquantitative picture from uncertainty principle Ground state solution * Sphericallysymmetric excited states (sstates) * * contains details beyond what we expect you to know on exams. Lecture 16, p 6 Quantum Particles in 3D Potentials So far, we have considered quantum particles bound in onedimensional potentials. This situation can be applicable to certain physical systems but it lacks some of the features of most real 3D quantum systems, such as atoms and artificial structures. One consequence of confining a quantum particle in two or three dimensions is degeneracy  the existence of several quantum states at the same energy. To illustrate this important point in a simple system, lets extend our favorite potential  the infinite square well  to three dimensions . A real (2D) quantum dot http://pages.unibas.ch/physmeso/Pictures/pictures.html Lecture 16, p 7 Particle in a 3D Box (1) outside box, x or y or z < 0 outside box, x or y or z > L inside box U(x,y,z) = Lets solve this SEQ for the particle in a 3D cubical box: The extension of the Schrdinger Equation (SEQ) to 3D is straightforward in Cartesian (x,y,z) coordinates: This U(x,y,z) can be separated: U(x,y,z) = U(x) + U(y) + U(z) y z x L L L ( , , ) x y z where Kinetic energy term: ( 29 2 2 2 1 2 x y z p p p m + + U = if any of the three terms = ....
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 Spring '11
 MESTRE
 Magnetism

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