Download Assignment 5 Questions - Quantum Mechanics I | PHY 389K and more Assignments Quantum Mechanics in PDF only on Docsity! Pls, 329K HW S 10/5106
) “the al ys of an obrrcerrahle A au fe wen ahedey
ah sefinad wh = (cyiaeiv) ~ Cv ay)?
Cobrifade i sabe of ide ah Ateyable Z - &.7
am le pdade
@) Wy = lA, Ms 0) fx avtiok ds * ef A Ho talud O
4) Yy = 14 meg) I I és at ton S
tapi of tote Hat, ed fod He
otis § fox “ umcrrtoinhits bry, 04 in Le iy bi
2. Find the matrix elements <a IS] ¢ > of the three operators S;
commutation relation,
[$i 5;] = tege Se
and the anticommutation relation
{5),5)} = 5:8; + 358. =alby
3. Calculate the matrices <j = 1,m[Jjlj = 1m’ >, (for m,m' = 7 = 1,0,-1;7 = 1,2,3)
a. pelos the new basis vector €, in the space R=! by
= 1,2,3 which fulfill the
2 aslo th sha s-l ay
and aleulate the matrices
{e,|Jiles), 7? = 12,3
(let + label the rows and s the columns of the matrix as defined as p.20 of text)
3, a) Show that
(er|Jijlea) = c(djrdis ~ dirdjs) where Jyj = exgete (i748 = 1,2,3)
and determine the number ¢.
b) Is there a relation between the e, and the three basis vectors of a cartesian basis system in the 3
dimensional space?
6. Construct normalized eigenvectors
i =tm >= alj =4,m=)> +67 =$,m =>
such that the |j,m, > are simultaneous eigenvectors of J” and J) satisfying
Pj >= li + bd, >
Aylgmy = mqlj,27 >
Calculate the allowed values of mm: -
T. Consider electromagnetic dipole decays of a diatomic molecule that rotates
a) Show that the frequency #j41.; of the photon emitted in such a decay is given by
Miinny Sate U1)
b) The experimental values for v;,;.; are tabulated below for HCI: in the far infrared. Determine the
moment. of inertia of the HCl system
¢) What is the energy of the j = | eigenstate?
@) Use the value of the moment of inertia determined from the data and the atomic weights of (1(35.45)
and H(1.008) to calculate the distance x between the H and the Cl in the HCI molecule.
8. Calculate the commutator [L;, Q,] if the angular momentum J; is given by Lj = ¢jpQjP%, where Pi
and Qj fulfill the c.r, (2.1) of chapter TH.
( Table )
ao # 5 & 7 e Z fe i
Yaw] 93,038 (e#s3 WHAT 14587 BERT Hg a3 20660 2808S
