hw8 - CHAPTER7 THE ONE DIMENSION 81 LS 1 lnewJAs in...

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CHAPTER 7. THE SCHR6DINGER EQUATION IN ONE DIMENSION 81 LS! 1 lnewJ As in Eq. (7.105), the required probability is p : s-2ar,, where, according to Eq. (7.102), the exponent is 2L _zat, = __F ,,/2rn(U. - E) : -= r/2mcz(U, _ E) ' tu:.' 8nm 197 eV.nm \/ 11.022 x 100 eV) x (3 eV) = -71.1 \tr""A6-E 70 fm 197 MeV.fm @=-68.be fng"O:grtg4.obability of escape in a single collision with the surface p(l collision) = 6*6E.5e J t.Oa x fO-so l. The probability in a day is P(l day) P(l collision) x (number of collisions in a day) (1.63 x 10-30) x (b x 1021 x 3600 x 24) :lt;;o=l 7.56 r [new] Ftom Euler's relation, eid cos 0 + isind, it follows that ettr cos 7r + isinTr : _1. ?57 o II V @,t) : g(x)e-iEt/h, then mff n 1t1x1 (#) u*,,^ Et,(de-dEt/ h (##* ut')) t :[(-*,#* u(')) ,,b61]"-nn'ra *1,(r)e-iE lh (r) (ID rparing Eqs. (I) amd (II), we see that the two right-hand sides are equal. Therefore the two sides are equal, and this is the time-dependent Schr6dinger equation o Since t/n and, l.,z are normalized, we know that I bhl2 iln I ltp2l2h: 1, where the als run from 0 to a. Also, if we make the change of variables a ni/o, f". 2 f't 1tt Jo rltrrlra, = i Jo "in"o sinms dy 1"""{" rn)U cos(n + rn)Uldg 0 in the second equality we used the trig identity for sindsin/.

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This note was uploaded on 02/10/2010 for the course PHSY 70 taught by Professor -1 during the Fall '10 term at Stanford.

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hw8 - CHAPTER7 THE ONE DIMENSION 81 LS 1 lnewJAs in...

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