228s13-l17

# The radial wave function rr must go to 0 at large r

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Unformatted text preview: ), which you might have encountered elsewhere. The are of the form of Legendre polynomials times e±imφ. (Actually solving the equations is too much math for us.) Monday, April 1, 2013 The Hydrogen Atom For hydrogen, like the spherical box, we have spherical symmetry, but the potential energy is the Coulomb potential energy between opposite charges: U(r) = -e2/4πε0r. The radial wave function R(r) must go to 0 at large r, since the electrons are bound to the protons, but does not necessarily go to 0 at the origin. The angular functions must be ﬁnite and periodic in φ, with a period of 2π. The wave functions are characterized by 3 quantum numbers ... Monday, April 1, 2013 The Principal Quantum Number n = 1, 2, 3, ...: The wave function is of the form of a polynomial series in r (∑i=0,...n-1 ciri) (some ci are 0) times an exponential exp(-r/na0). Here a0 is the Bohr radius, 0.053 nm. The resulting energies are the same as in the Bohr model, En = -13.6 eV / n2. n=2 n=3 examples of wa...
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## This document was uploaded on 02/18/2014 for the course PHYS 228 at Rutgers.

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