Midterm 3 Solutions

Thus n sy q 1 s rhq j l y 0 n h qln n split

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: sis 0 1 0 001 ¬༼ be careful of this term ` ` Â` Sy = - 2 JS+ - S- N Ø8 j, mz \< basis `2 Sy Ø8 j, mz \< basis `3 Sy Ø8 j, mz \< basis 0 - 0  0 - 0Â0 — 2 1 0 -1 020 -1 0 1 0 -2  0 —3 2  0 -2  22 0 2 0 —2 2 ` = —2 S y ` `n So Sy does not square to the identity, but Sy as a function of n does have a period of 2 (up to normalization and excepting n = 0, which is the identity). Thus `n Sy Âq ` ` 1 -S RHq j L = ‰ — y = ⁄¶= 0 n! H- qLn n ¬༼ Split into identity term and the rest into n-even/odd — ` 2m Sy ` 1 = 1ཽ + ⁄¶ = 1 H2 mL! H- qL2 m m — 1 + ⁄¶ = 0 H2 m + 1L! H- qL2 m + 1 m `2 Sy — H-1Lm -  B⁄¶ = 0 H2 m + 1L! q2 m + 1 F m = cos q - 1 ` RHq j L Ø8 j, mz \< basis ` Sy — = sin q 100 010 001 + 1 2 1 0 -1 Hcos q - 1L 0 2 0 -1 0 1 -  2 0 - 0 sin q  0 - 0Â0 Therefore 1 2 ` RHq j L Ø8 j, mz \< basis H1 + cos qL 1 2 — ` JS y ê—N ` 2 = JS y ê—N ` H-1Lm = 1ཽ + B⁄¶ = 1 H2 mL! q2 m F m ` 2m+1 Sy sin q 1 2 1 Printed M sin q by H1athematicaqfL Students - cos or 2 cos q - 1 2 sin q 8 MidtermExam3Solutions.nb Therefore 1 2 ` RHq j L Ø8 j, mz \< basis H1 + cos qL 1 2 1 2 sin q H1 - cos qL 1 2 sin q 1 2 cos q 1 2 sin q H1 - cos qL - 1 2 1 2 sin q H1 + cos qL and we have ` 1, 1n \ = RHq j L 1, 1z \ = 1 2 H1 + cos qL 1, 1z \ + 1 2 sin q 1, 0z \ + 1 2 H1 - cos qL 1, -1z \ ü Part b We see from (a) that the fraction of particles that survive the third measurement will be maximized at 1 16 when sin4 q = 1 p fl q= 2 ü Part c The fraction of particles that survive the last measurement if the SGn device were removed is zero as 1, ± 1z \ are orthogonal. ü Statistics Mean = 5.22 Stddev = 3.00 Printed by Mathematica for Students MidtermExam3Solutions.nb Total Mean = 16.11 Stddev = 7.51 Printed by Mathematica for Students 9...
View Full Document

This note was uploaded on 02/01/2014 for the course PHYC 491/496 taught by Professor Akimasamiyake during the Fall '13 term at New Mexico.

Ask a homework question - tutors are online