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Unformatted text preview: (a) Rewrite the radial wavefunction as R(r) = u(r)/r, and by substituting into the equation above, obtain a differential equation for u. What is the advantage of doing this transformation? (b) The infinite spherical well is give by the potential V(r) = 0 for r a, V(r) = for r &gt; a. Draw the effective potential appropriate for the Schrodinger equation describing the function u for the quantum values l = 0, l = 1 and l =2. For the values l = 0 and l = 1, draw the corresponding eigenstate wavefunctions. How are these wavefunctions related to the quantum number n for the radial wavefunction? (c) Find the eigenstates and eigenenergies associated with u for l = 0 (the familiar case). Keep in mind that the actual wavefunction is R = u/r and that it should not blow up at r = 0. (The solutions for general l are known as Bessel functions See Griffiths 4.1.3)...
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 Fall '08
 Staff
 Quantum Physics, Schrodinger Equation, Spherical Harmonics, 2L, spherical harmonics Yl

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