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Birla Institute of Technology and Science, Pilani, RajasthanFirst Semester 2006-200

!om"rehensi#e $%amination &!losed Boo'(Course Title: Computational Physics Course No. PHY C 232

Time: 180 mins 12-12-2006 Total mar s: 120

1. Consi!er a potential step o" the "orm sho#n in the "i$ure %elo#.

The potential is &ero to the le"t o" the ori$in' %ut has a constant(alue ) to the ri$ht. *uch a potential step mi$ht occur at the sur"ace o" a metal +"ore,ample .

a rite !o#n the *chro!in$er #a(e e/uation "or each o" the t#o re$ions. % Consi!erin$ ener$y ei$en(alues )' #rite !o#n the $eneral solution "or

each re$ion.c rite !o#n the %oun!ary con!itions "or this situation.! se the %oun!ary con!itions to eliminate as many un no#n constants as

possi%le. + , 416

2. 5t is !esire! to "in! the roots o" the f(x) %y the Ne#ton- aphson metho!' #here0122-+ 3 =+= x x x x f

hat startin$ (alues "or the root #oul! cause Ne#ton7s metho! to "ail totally inthis case *ho# +an! e,plain all the calculations use! to o%tain the ans#er.

+10

3. 9eri(e e,pressions "or the error in(ol(e! in usin$ the trape&oi!al rule "ornumerically inte$ratin$ "unctions in one an! t#o !imensions. +1

. particle mo(es un!er a constant $ra(itational "orce. The e/uation o" motion "orthe particle is inte$rate! usin$ uler7s metho! to o%tain the (elocity as a "unctiono" time. hat #oul! %e the error in usin$ the uler metho! in this case hyHo# #oul! the situation chan$e i" air resistance #ere consi!ere! +10

;. 5t is !esire! to numerically sol(e the

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re/uire! "or one complete iteration o(er the entire $ri!. =i(e all the steps in(ol(e!in arri(in$ at the ans#er. +10

6.