phy246s11_hw4_sol

phy246s11_hw4_sol - Physics 246 Fourth Homework Set Due...

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Physics 246 Fourth Homework Set Due: February 1$, 2911 1. Sometimes we can construct eigenvectors of non-Hermitian operators. This problem provides an example. a) Show that lo >: exP(aa+)ln:0 > (where e,at,n have the usual meaning) is a (right) eigenvector of a. What is the eigenvalue? b) Correspondingly < o'lo+ :( a'l(number) What is the number and what is the form of < u'l ? c) Compute < a,la > d) Evaluate < a-lllla > -----------:-i- < CI*la > and Af/. ; :i 2. A particle of mass m and energy E : t-t2 l2ma2 moves through a series of ly' one- dimensional regions. The (constant) potential in the nth region is I/ : (t - nz)E where ?? : 1, 2,. . .. The first and -l{th regions have infinite width while the intermediate ones have width zro. Calculate the transmission coefficients for a particle entering from either end and compare the two. 3. Probiem 3 is on the other side of the paper.
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d, Another way to solve so that lq,pl -- i and where AIso define r-* ln r-+\l -q uma H :2h,wJz J, -- 11p2
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phy246s11_hw4_sol - Physics 246 Fourth Homework Set Due...

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