Quantum Mechanics of the Hydrogen Atom: Problems and Solutions, Slides of Quantum Mechanics

Download Quantum Mechanics of the Hydrogen Atom: Problems and Solutions and more Slides Quantum Mechanics in PDF only on Docsity! Homework this week: • HW #18 Thursday Nov 10 by 10pm Quantum mechanics docsity.com Exam 2 Phys 451 84 / 100 Class average 18.4 / 100 Problem 1 15.2 / 100 Problem 2 17.2 / 100 Problem 3 16.2 / 100 Problem 4 16.9 / 100 Problem 5 Highest score 96 / 100 docsity.com Quantum mechanics The hydrogen atom 0 ( ) jj j v c        jj c ljj nlj c 221 )1(2 1    Equivalent to associated Laguerre polynomials )2()( 12 1    l lnLv   )(1)( xL dx d xL q p pp pq         qx q x q xe dx d exL       )( Pb 4.12 docsity.com Quantum mechanics The hydrogen atom      , , ,nlm nl mlr R r Y     Spherical harmonics (table 4.3) Legendre polynomials Radial wave functions (table 4.7) Laguerre polynomials 0 ( ) jj j v c        jj c ljj nlj c 221 )1(2 1    OR Power series expansion with recursion formula docsity.com French mathematicians Quantum mechanics • Edmond Laguerre 1834 – 1886 • Adrien-Marie Legendre 1752 – 1833 docsity.com Quantum mechanics The hydrogen atom Representation of   ,,rnlm Bohr radius 2 100 2 4 0.529 10a m me     docsity.com Quantum mechanics The hydrogen atom Expectation values      , , ,nlm nl mlr R r Y     2 2r r R r dr  22 2 2r r R r dr  2 2sin cos sinx d d r R r dr        Pb 4.13 Most probable values Pb 4.14  2 2 max r 2 2 0 d r dr   docsity.com Quantum mechanics The hydrogen atom Expectation values for potential      , , ,nlm nl mlr R r Y     2 2 2 04 e V R r dr r         Pb 4.15 docsity.com Quantum mechanics The hydrogen atom 2 1 n E En  na kn 1  Energies levels Stationary states   ),()(,,  mlnlnlm YrRr  n: principal quantum number l: azimuthal quantum number 1 nl m: magnetic quantum number lm  Degeneracy of nth energy level: 1 2 0 2 1 n l l n     docsity.com Quantum mechanics The hydrogen atom 1 2 2 13.6 n E eV E n n   Energies levels Spectroscopy          221 11 fi nn E hc E  Energy transition E 0 E1 E2 E3 E4 Lyman Balmer Paschen          22 111 if nn R  Rydberg constant 7 11.097 10R m  Pb 4.16 Pb 4.17 docsity.com Quantum mechanics Quiz 25 A. 465 nm B. 87.5 x 10-8 m C. 4.65 mm D. 87.5 x10-7 m E. 4.65 x 10-8 m What is the wavelength of the electromagnetic radiation emitted by electrons transiting from the 7th to the 5th band in the hydrogen atom? 7 11.097 10R m  docsity.com