pset6 - is a constant with units of energy × distance. (a)...

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University of Central Florida Department of Physics Fall 2009 PHY 4604 Problem Set # 6 Due: November 16, 2009 1. Libof , 6.33 2. Libof , 7.3 3. Libof , 7.8 4. Libof , 7.16 5. Using the algebraic method, compute the matrix elements in the energy basis of the position and momentum operator, ˆ x and ˆ p , for a one-dimensional harmonic oscillator. Using the same method, evaluate a ˆ x A , a ˆ p A , a ˆ x 2 A , a ˆ p 2 A , and Δ x Δ p for an energy eigenstate | n A . How do your results compare with the Heisenberg uncertainty principle? 6. Libof , 7.37 7. Libof , 7.38 8. Libof , 7.57 9. Consider a particle of mass m in one-dimensional subjected to a Dirac delta-function potential, V ( x ) = g δ ( x ) , where g
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Unformatted text preview: is a constant with units of energy × distance. (a) Show that the appropriate boundary conditions of the energy eigenfunctions in this case are of the form, ψ ( x = 0 + ) = ψ ( x = 0-) = ψ (0) and ¯ h 2 2 m b dψ dx (0 + ) − dψ dx (0-) B = g ψ (0) . (b) Use these boundary conditions to ±nd bound states when g < 0 (attractive poten-tial). How many bound states are there? (c) Use the same boundary conditions to ±nd the transmission of re²ection coe³cients of the plane waves scattered by this potential. Does it matter if g is positive or negative?...
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This note was uploaded on 11/09/2009 for the course PHY 4604 taught by Professor Mucciolo during the Spring '09 term at University of Central Florida.

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