Question

[Finite potential well] Consider a symmetric square well potential of a finite depth, i.e., V(x) = 0 inside the well, V(x) = V outside the well. NOTE: for a general discontinuous potential the boundary conditions are the continuity of both the wave function and its first derivative at the point(s) of the discontinuity of the potential y (x_)=y(x),y'(x_)=y'(x4) (i) What are the functional forms of the solutions for y(x) inside and outside the well?

Answer 1

( if tift FGID assuming ECU (a) + " + vyzE4 for (in & Gu) 4 = A è n + Be where r = -2m (B-v) for regison (1) as n as 4 = A em + Bernat => B=0 .: 46m)= tern for uza for u a ie region 3.0 plu) = A enn + Bern as assuri for 27 Р.): g'е - 7, region (ii) - to YH = E => QUE zmy => Y = cek + De la where I am znikniku

4an2=S Aern n<-a 9 cellen Deken -acuza ka (6) Bondary conditions a (1969-) = 41-9+) Ara = Eelika De" () Pla-)= Y(at) Celka + Deiker = Bery (eu) w(-9-) = 4'(-4+) 1 v.Arra - ik ceka _ik De (0) 4'ca-) = 4(at) ik celka Delka = -r Be (c) 2Y frob. of finding ontride well is t o R ru du = À 1 ezrno (usa) 28 = À ezra toriget ride as well is

for r o probability is to Xo ra len ora = o po =) pio v zm (-E) is woro. p >0,