PHY 356 - Homework 1 Solution
I.
PROBLEM 1 (TOWNSEND 1.7)
a) The up state for the SGn device is given by
|ni = cos
| + zi + sin
| zi .
2
2
(1)
The first need the fraction of particles that pass through the first device. This is given by the probabilit
Using a Mach-Zehnder Interferometer to Illustrate Feynman's
Sum Over Histories Approach to Quantum Mechanics
Frank Rioux
Department of Chemistry
CSB|SJU
Thirty-one years ago Dick Feynman told me about his 'sum over histories'
version of quantum mechanics.
Prof. Aephraim Steinberg
Physics 356F: Problem Set #1
assigned 25 September 2012
(due at the start of your tutorial section the week of
October 8, 2012)
1. Problem 1.7 from the textbook
2. Problem 1.8 from the textbook
3. Problem 2.10 from the textbook
4.
Prof. Aephraim Steinberg
Physics 356F: Problem Set #2
assigned 23 October 2012
(due the week of 6 November 2012 at the start of your
tutorial)
1. problem 6.9 (or 6.8 from the 1st edition)
2. problem 6.19 (or 6.16 in the 1st edition)
3. (a) Show from the d
1
mardi 9 octobre 12
1
Quantum jumps
2
mardi 9 octobre 12
2
(1952, 26 years after
his equation, nearly
40 years after Bohr
model)
3
mardi 9 octobre 12
3
Schrdinger remarked to Bohr that
"Had I known that we were not going to get rid of this damned
quantum
FIRST:
jeudi 22 novembre 12
1
jeudi 22 novembre 12
2
The information content of a quantum
Quantum dense coding
Bell-state measurement
Teleportation (polarisation states)
A few words about quantum computing
Quantum error correction?
More quantum eraser
More Bohr-Einstein debates
Einstein:
I can't believe God plays
dice with the universe.
Bohr:
Albert, stop telling God
what to do.
mardi 6 novembre 12
1
Einstein, Podolsky, & Rosen (1935)
Source
Alice
Bob
2 particles emitted together at the same
time with
More information content of a quantum
Teleportation (polarisation states)
The general idea of quantum info. processing
Grovers algorithm; some mention of Shors
Quantum error correction
Teleportation (continuous variables)
2 Nov 2009
mardi 27 novembre 12
1
Uses of photon uncertainty
The Problem of
Cryptography
Classical Cryptography
The only provably secure way to send secrets:
the "one-time pad." Alice and Bob share a random
"key", which is AS LONG AS THE ENTIRE MESSAGE.
They never reuse it. (Soviets m
Illustrating the Superposition Principle with Single Photon Interference
Frank Rioux
Department of Chemistry
St. Johns University
College of St. Benedict
St. Joseph, MN 56374
Abstract
Single-photon interference in a Mach-Zehnder interferometer is used to
Prof. Aephraim Steinberg
Physics 356F: Problem Set #2
assigned 29 September 2014
(due the week of 6 October 2014 at the start of your
tutorial)
1. problem 3.17
2. problem 3.15
3. problem 3.16
4. (a) Show from the denition of the commutator that [AB, C] =
Prof. Aephraim Steinberg
Physics 356F: Problem Set #3
assigned 10 October 2014
(due 21 October 2014 [solution sets will be posted by the
end of the week, for midterm review, so no extensions
will be possible beyond noon on Thursday the 23rd])
1. (a) Suppo
Prof. Aephraim Steinberg
Physics 356F: Problem Set #1
assigned 12 September 2014
(due the week of September 22, at the start of your
tutorial section)
.
Since an overall phase has no measurable eect, we can take = a and = bei , where
a, b, and (and hence
Prof. Aephraim Steinberg
Physics 356F: Problem Set #5
assigned 21 November 2014
(due by noon on Tuesday, 2 December 2014)
Note: There will be one more, short, not-for-credit, problem set to cover the material
from the last week of class. It will not be ma
CD
139%356 r ?RQT$L&U\ SET 575% Saumumi I” 2‘1 UCTvZQ’V‘f
H . . :.Ii.Hi"'->ij. 1;} if. . LT.” . . I
p2 6&3 _
H . a: I. '1 i I ii. .i I: i. . I I: I , ' I. . I: .
3L) ’05 COJCM l3 .flacasiscur "‘"l Sihu
vial—t I B an 8-:EL7L453Za-(Q ‘7 Lfl E] +La cmlj
Pos
?HYg56 733741 éfiogw¥fm O
f. a.) TA fad .7“me mam/a =. Maw/7* .c¢.cwgwhmz~%.
. aux (0*, [a] We
=5 i[/1 =. I}; / .
a ' (aw J ._._/a+¥’é m )
=> (odefi/ )(Ll+[?a—F4 (a- LJ-ef‘l “CPL-e I
v) a.'.*.‘a:1‘ .0 9’ (6"?! Mia”) f— a?+L=1~— aé {e‘7+e“'7/
7L.) S
G)
'PH‘TBSG fissxguMEgT =i1J=~S Ecuxuaps 1 Dec, at,”
MW
H .I I I. I I. I %. fly? '(n. Z .I .I i: I
' * L (M\ (UL-t 0*) [FIND
" :(r—‘w, "m, fjfimflq . . . .
' " . B's/ET”! LS > '
_k k JmJa—SIW'HNH-l).f
. 2M“) . {ma-nHH).
I J};- H . J Jqu
LL\.M{V~\ wwl
Prof. Aephraim Steinberg
Physics 356F: Problem Set #4
assigned 7 November 2014
(due Thursday 20 November at the start of tutorial)
1. problem 6.9
2. problem 6.11
3. problem 7.4
4. problem 7.7
5. From your knowledge of the raising and lowering operators an
