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Lect12 - "Anyone who can contemplate quantum mechanics...

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“Anyone who can contemplate quantum mechanics without getting dizzy hasn’t understood it.” --Niels Bohr
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Final Exam – March 3! Overview of the rest of the course Up to now – general properties and equations of quantum mechanics Time-dependent and time-independent Schr. Eqs. Eigenstates, superposition of eignestates and time- dependence, tunneling, Schrodinger’s cat, . . . This week – quantum states in 3 dimensions, electron spin, H atom, exclusion principle, periodic table of atoms Next week – molecules and solids, consequences of Q. M. Metals, insulators, semiconductors, superconductors, lasers, . . HW 6 due next Thursday, 8am
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Angular Momentum, Atomic States, Spin, & the Pauli Principle -15 -10 -5 0 0 5 10 15 20 U(r) n= 1 n= 3 n= 2
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Overview Overview z Schrödinger’s Equation for the Hydrogen Atom z Radial wave functions z Angular wave functions z Angular Momentum z Quantization of L z and L 2 z Spin and the Pauli exclusion principle z Stern-Gerlach experiment z Nuclear spin and MRI
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Summary of s Summary of s - - states of H states of H - atom atom z To get the exact eigenstates and energies for the “s-states” of the Coulomb potential, one needs to solve the radial SEQ z Summary of wave functions for the “s-states”: z The zeros in the subscripts below are a reminder that these are states with zero angular momentum. 0 r 0 4a 0 R 10 0 / 0 , 1 ) ( a r e r R r R 20 0 10a 0 0 0 2 / 0 0 , 2 2 1 ) ( a r e a r r R R 30 r 0 15a 0 0 3 / 2 0 0 0 , 3 3 2 2 3 ) ( a r e a r a r r R + ) r ( ER ) r ( R r e r r r 1 m 2 2 2 2 2 = κ = (spherically symmetric)
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