PHY2D_Quiz8

# PHY2D_Quiz8 - the interface(b Is the relation R T = 1...

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QUIZ 8 PHYSICS 2D SPRING QUARTER 2009 Professor S.K.Sinha Formulas and constants Mass of electron m e = 9.1. 10 -31 kg Charge on electron = 1.6.10 -19 C Planck’s Constant h= 6.626. 10 -34 J.s =4.136. 10 -15 eV.s h = h / 2 ! = 1.055.10 " 34 J . s = 6.582.10 " 16 eV . s 1 eV =1.6. 10 -19 J Coulomb’s constant k = 1/ (4 !" 0 ) = 8.99.10 9 N . m 2 / kg 2 Velocity of light c = 3.10 8 m/s Energy of photon E = hf Momentum operator p = ! i h " " x Stationary Schrodinger Equation ! h 2 2 m d 2 " dx 2 + U ( x ) = E Electron current through unit area for free electrons = nv A 2 where n= number density of electrons; v = velocity of electrons; A =amplitude of plane wave. SHOW ALL DETAILS OF YOUR DERIVATIONS! 1. A current of electrons each with total energy 10 eV traveling in a material where the potential is 6 eV is incident on an interface with a metal where the potential energy is 0 eV. (These energies are non-relativistic) (a) Derive the expressions for and calculate the numerical values of the transmission coefficient T and the reflection coefficient R for the electrons at

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Unformatted text preview: the interface. (b) Is the relation R + T = 1 obeyed? Comment on your answer. (10 points) 2. Consider the square barrier potential , where the potential = 0 for x < 0, the potential = U for 0 < x < L and is 0 for x > L. (U is positive). An electron of energy E is incident on the barrier from the region x < 0. (a) write down general expressions for the electron wavefunction in the 3 regions : x <0, 0<x< L and x>0 in terms of constants involving U and E. (You do not have to solve for the amplitudes) (b) write down 4 conditions the amplitudes of these wavefunctions have to satisfy. (c) If 2 m h 2 ( U ! E ) L >>1 (i.e. if (U-E) is very large or L is very large) show that the conditions are satisfied to high accuracy if the amplitude of the final transmitted wave is zero, and that in this case the reflection coefficient R becomes 1. (15 points)...
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## This note was uploaded on 12/07/2009 for the course PHYS phys 2d taught by Professor Hirsch during the Spring '08 term at UCSD.

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PHY2D_Quiz8 - the interface(b Is the relation R T = 1...

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