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hw.5 - The standard trick is to first differentiate the...

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Physics 829 Spring 2001 Dr. Herbst Homework Assignment # 5 Due: 4 May 2001 1) Use the WKB method to determine the transmission coefficient for tunneling by a particle of mass m under a one-dimensional potential barrier of the type: V(x) = V 0 (1 - x 2 /x 0 2 ) if |x| < x 0 ; V = 0 elsewhere. Assuming the particle to be an electron, V 0 to be 10 eV, and x 0 to be 2 Å, determine the actual transmission coefficient for E = 6 eV. 2) Determine, in the WKB approximation, the discrete energy levels for the potential V(x) = -V 0 /cosh 2 (x/c). This involves a difficult integration.
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Unformatted text preview: The standard trick is to first differentiate the integral (call it I(E)) with respect to E (this is actually permissible), and then integrate the new integral to determine an analytic form for dI/dE. Determination of I(E) follows with an indefinite integration. 3) Compare the WKB and actual wave functions for the ground state of the harmonic oscillator in one dimension. You need not worry about the regions right next to the turning points....
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