Lect17 - Anyone who can contemplate quantum mechanics...

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Lecture 17, p 1 “Anyone who can contemplate quantum mechanics without getting dizzy hasn’t understood it.” --Niels Bohr
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Lecture 17, p 2 Special (Optional) Lecture “Quantum Information” One of the most modern applications of QM quantum computing quantum communication cryptography, teleportation quantum metrology Prof. Kwiat will give a special 214-level lecture on this topic Sunday, Feb. 27 3 pm, 141 Loomis Attendance is optional, but encouraged.
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Lecture 17, p 3 Final Exam: Monday, March 7 Homework 6: Due Saturday (March 5), 8 am Up to now: General properties and equations of quantum mechanics Time-independent Schrodinger‟s Equation (SEQ) and eigenstates. Time-dependent SEQ, superposition of eigenstates, time dependence. Collapse of the wave function, Schrodinger‟s 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
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Lecture 17, p 4 Lecture 17: Angular Momentum, Atomic States, Spin, & Selection Rules
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Lecture 17, p 5 Today Schrödinger‟s Equation for the Hydrogen Atom Radial wave functions Angular wave functions Angular Momentum Quantization of L z and L 2 Spin and the Pauli exclusion principle Stern-Gerlach experiment
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Lecture 17, p 6 Summary of S-states of H-atom The “s-states” ( l =0, m =0) of the Coulomb potential have no angular dependence. In general: because Y 00 ( q , f ) is a constant. Some s-state wave functions (radial part): r R 20 0 10a 0 R 30 r 0 15a 0 0 5 1 r 0 4a 0 R 10           00 0 , , , : , t , bu nlm nl lm nn r R r Y r R r q f S-state wave functions are spherically symmetric. | 20 (r, q , f )| 2 : http://www.falstad.com/qmatom/
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Lecture 17, p 7 The Y lm ( q , f ) are known as “spherical harmonics”. They are related to the angular momentum of the electron. Total Wave Function of the H-atom We will now consider non-zero values of the other two quantum numbers: l and m . n “principal” ( n 1) l “orbital” (0 l < n-1 ) m “magnetic” (- l m + l )       , , , nlm nl lm r R r Y q f x y z r q f * The constraints on l and m come from the boundary conditions one must impose on the solutions to the Schrodinger equation. We‟ll discuss them briefly. *
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Lecture 17, p 8 Quantized Angular Momentum Linear momentum depends on the wavelength (k=2 p / ): Angular momentum depends on the tangential component of the momentum. Therefore L z depends on the wavelength as one moves around a circle in the x-y plane. Therefore, a state with L z has a similar form: An important boundary condition: An integer number of wavelengths must fit around the circle.
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This note was uploaded on 04/04/2011 for the course PHYSICS 214 taught by Professor Mestre during the Spring '11 term at University of Illinois at Urbana–Champaign.

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Lect17 - Anyone who can contemplate quantum mechanics...

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