Final-FS01

# Final-FS01 - Phys 208 Theoretical Physics Final Exam Dec 10...

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Phys 208 – Theoretical Physics – Final Exam – Dec. 10, 2001 1. (25 pts) a) Find and plot the roots of . 8 3 b) Evaluate . sin( ln ) π 2 2 + i 2. (25 pts) a) Evaluate the derivative . () d dx xe x 100 100 2 b) Show that . xe d x n a na x n + = ! 1 0 3. (25 pts) The excited state 2 p radial wave function of a hydrogenic atom/ion of nuclear charge Ze is given by , where N is a constant and is the Bohr radius. Rr N r e p Zr a 2 2 0 / = a 0 a) Determine the most probable value of r for this atom/ion. b) Determine the normalization constant N . 4. (25 pts) Determine a general result for the integral . ( ) 53 32 1 1 xx P x d x + l 5. (25 pts) The Laguerre equation is , where the range of is xL x L nL nn n ′′+ − ′ + = 10 x given by and . The solutions are called Laguerre 0 << x n = 0123 ,, ,, L Lx n polynomials. a) Show that the Laguerre equation can be written as . e d dx xe L nL += 0 b) Prove that the functions are orthogonal on with respect to the n (, ) 0 weight function .

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Final-FS01 - Phys 208 Theoretical Physics Final Exam Dec 10...

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