phy246s11_hw6sol

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

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

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

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

View Full Document

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

View Full Document

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.

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
Ask a homework question - tutors are online