phy246s11_hw6sol

phy246s11_hw6sol - H and tr. a. Write // and L interms of...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Physics 246 Sixth Homework Set Due: March 4,20L1 1. Consider the square well barrier of height I/o and width 2a. a. One should get the result for delta function scattering by taking I/s -) @, @ * 0, ZaVo ' Vo. ExPlain. b. Get t/,, rltl and hence R,T by taking this limit of class rbsults for the barrier. c. Show that these satisfy the Schrodinger equation with boundary conditions ,hG) - rh?e) aub f #l-' :#vo1'(o) 2. Consider the Hamiltonian '^2^2 H- + +3*V(q-rr). 'lmt Zmz a. Show that in general [I/,p1] and lH,prl are nonzero. b. Show that in terms of p -- Pt * p2,, x - Irlrfrr * trlzitz nxt * m2 p _ rnzpt : rntpz, tr _ tr! _ 12 ft\ * TrL2 [P, X] : W,r] : -i,h arc the only nonvanishing commutators amongst this set. c. Find H (P,p, X, n). d. What is the CSCO of this system? Assume that V has only bound states (no continuum states). 3. Consider a two dimensional isotropic SHO. Take the CSCO to be
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

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

View Full DocumentRight Arrow Icon
Background image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: H and tr. a. Write // and L interms of ai and o!11 - L,2) where the only nonvanishing commutators are t ai, all _ 6rj. 1,. b. Rewrite ^f/ and L irnterms of &+: [email protected]+i,a2) and their adjoints. Compute the commutators of H and ^L with @a and A, at where A - &tat. c. Use b) to inf,er the complete spectrum of H and .L. d. Construct the eigenket'corresponding to Er* in terms of al and .4t nannei}ffi *)ffitt bz : "%* -L--+ J ",,l-X,q.-;**E' */e'r'e*t I =o I l_ k-o\l C sCO,o l,{.p. )) qe'g+Ll LLJfiI' .a [,r*o- L\*"_]'C Lrftrt^>: [*t+,^fi]tE = r(L^:+ )lD It^)* t{ A\*) = (t*-11,q tD N0r^/ , t*,J, ;,@,4u" ffiUr*/-fid. f"-,tra, d^i^nq; .,\ 0 Cd LIC'o l,i[o)= tdt* _ \ 0+;n'A itffi* -b -'#a, d* (tl'* '4 o^q/tr e{^'e u f^*Y fi .il Lt^ tl*\ ttr = 0, tl ,).,. ,'\tl 9J, It, 11 ," , *'* L arq gn n v"a, qst o) =O...
View Full Document

This document was uploaded on 03/23/2011.

Page1 / 6

phy246s11_hw6sol - H and tr. a. Write // and L interms of...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online