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

This preview shows pages 1–2. Sign up to view the full content.

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/.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 5

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online