Module405 »
Home Page
Supplementary physics course material wiki
|
|
Home PageModule405.HomePage HistoryHide minor edits - Show changes to output Changed line 32 from:
* Monday to:
* Monday 19 October - '''Exam study session''', 2pm 3rd floor AV room Changed line 32 from:
* Monday 12 October - Exam study session, 10am 3rd floor AV room to:
* Monday 12 October - '''Exam study session''', 10am 3rd floor AV room Added line 32:
* Monday 12 October - Exam study session, 10am 3rd floor AV room Changed line 40 from:
*[[Attach:AdvQII2015_V3.1.pdf|Version 3]] to:
*[[Attach:AdvQII2015_V3.1.pdf|Version 3.1]] Changed line 38 from:
*[[Attach: to:
*[[Attach:AdvQII2015_V3.pdf|Version 3]] Changed line 38 from:
*[[Attach:AdvQII to:
*[[Attach:AdvQII_2015_V3.pdf|Version 3]] Changed line 38 from:
*[[Attach:AdvQII to:
*[[Attach:AdvQII_Mod405_2015_V3.pdf|Version 3]] Deleted lines 36-37:
*[[Attach:AdvQII(405)_2015_V3.pdf|Version 3]] Changed line 52 from:
*'''Assignment 3, due Friday 9 October'''. Problems 10.2, 10.6, 10.7, 10.8 [ to:
*'''Assignment 3, due Friday 9 October'''. Problems 10.2, 10.6, 10.7, 10.8 [homogeneous system: neglect trap and quantum pressure], 10.10 Changed line 52 from:
*'''Assignment 3, due Friday 9 October'''. Problems 10.2, 10.6, 10.7, 10.8, 10.10 to:
*'''Assignment 3, due Friday 9 October'''. Problems 10.2, 10.6, 10.7, 10.8 [neglect all potentials in Eq. (10.45) ], 10.10 Changed lines 52-53 from:
*'''Assignment 3, due Friday 9 October'''. Problems 10.2, 10.6, 10.7, 10.8, 10.10 to:
*'''Assignment 3, due Friday 9 October'''. Problems 10.2, 10.6, 10.7, 10.8, 10.10 Changed line 52 from:
*'''Assignment 3, due Friday 9 October'''. to:
*'''Assignment 3, due Friday 9 October'''. Changed lines 52-53 from:
*'''Assignment 3, due Friday 9 October'''. Problems to:
*'''Assignment 3, due Friday 9 October'''. Problems TBA Problems 10.2, 10.6, 10.7, 10.8, 10.10 Changed lines 45-48 from:
*'''Assignment 2, to:
*'''Assignment 2, Wednesday 30 September'''. 1. Derive (8.49) from (8.40). 2. Derive (8.51). 3. Problems 9.3, 9.4, 9.6, 9.7 Added line 31:
* Due to illness, I have been unable to give 9/9 and 10/9 lectures. Next week (14/9 - 18/9) is project week (Friday is the due day!). I will add an announcement about assignment 2 soon, but the aim is to not clash with your commitments next week too much. Changed line 46 from:
*'''Assignment 3, due Friday 9 October to:
*'''Assignment 3, due Friday 9 October'''. Problems TBA Changed lines 44-46 from:
*'''Assignment 2, due *'''Assignment 3, due to:
*'''Assignment 2, due Friday 25 September'''. Problems TBA *'''Assignment 3, due Friday 9 October '''. Problems TBA Changed lines 15-17 from:
*11am - 12pm *10am - 12pm to:
*Tuesday 11am - 12pm, G09 *Wednesday 10am - 12pm in 4th floor Video Conference room Changed line 17 from:
*10am - 12pm on Wednesday to:
*10am - 12pm on Wednesday 4th floor Video Conference room Changed line 17 from:
* to:
*10am - 12pm on Wednesday G400 Changed line 17 from:
* to:
*11am - 1pm on Wednesday G400 Added lines 29-30:
*'''18 August lecture cancelled''' (due to illness). New time later this week to be determined. * Assignment 1 now accepted until '''Friday 21 August'''. Changed line 28 from:
to:
*Assignment 1 now due 19 August (to further free up project week). Changed line 40 from:
*'''Assignment 1, due Wednesday to:
*'''Assignment 1, due Wednesday 19 August'''. Problems 4.4, 4.5, 4.6, 5.1, 6.4 Changed lines 13-17 from:
:'''REVISED TIMES''': 11am - 12pm on Tuesday G09 to:
:'''REVISED TIMES''': *11am - 12pm on Tuesday G09 *10am - 12pm on Wednesday G400 Changed lines 9-10 from:
''Prerequisites to:
:'''Prerequisites''': Module 404. PHSI 336 strongly recommended. :'''Lecturer''': [[http://www.physics.otago.ac.nz/research/btg/Site/DrAshtonBradley|Ashton Bradley]]. Room 416. Ph 4794121. ashton.bradley@otago.ac.nz :'''REVISED TIMES''': 11am - 12pm on Tuesday G09, 10am - 12pm on Wednesday G400 :'''Assessment''': 30% assignments, 70% Exam (Closed book). Changed lines 18-27 from:
\\ ''REVISED TIMES:'' 11am - 12pm on Tuesday G09, 10am - 12pm on Wednesday G400 \\ ''Assessment:'' 30% assignments, 70% Exam (Closed book). \\ to:
Changed lines 23-24 from:
Revised notes online below. (future changes will be kept minimal this semester). to:
*Revised notes online below. (future changes will be kept minimal this semester). Changed lines 29-31 from:
[[Attach:AdvQII(405)_2015_V1.pdf|Version 1]] to:
*[[Attach:AdvQII(405)_2015_V1.pdf|Version 1]] Changed lines 33-53 from:
''''' Assignments '''Assignment 1, due Wednesday 12 August Problems 4.4 from version 1 course notes linked above \\ Problems TBA Problems TBA to:
''''' Assignments (problems are from version 1 course notes linked above) ''''' *'''Assignment 1, due Wednesday 12 August'''. Problems 4.4, 4.5, 4.6, 5.1, 6.4 *'''Assignment 2, due Wednesday 2 September'''. Problems TBA *'''Assignment 3, due Wednesday 7 October '''. Problems TBA Changed lines 39-40 from:
'''Assignment 1, due Wednesday to:
'''Assignment 1, due Wednesday 12 August''' Changed lines 44-56 from:
from version 1 course notes linked above. to:
from version 1 course notes linked above. \\ '''Assignment 2, due Wednesday 2 September''' Problems TBA \\ '''Assignment 3, due Wednesday 7 October ''' Problems TBA Added line 6:
\\ Added line 11:
\\ Added line 14:
\\ Added line 17:
\\ Added lines 19-20:
\\ Changed line 24 from:
''''' to:
'''''Course notes''''' Changed line 38 from:
from to:
from version 1 course notes linked above. Changed line 12 from:
'' to:
''REVISED TIMES:'' 11am - 12pm on Tuesday G09, 10am - 12pm on Wednesday G400 Changed line 8 from:
''Prerequisites:'' to:
''Prerequisites:'' Module 404. PHSI 336 strongly recommended. Added lines 11-12:
''times:'' 11am - 12pm on Tuesday, 10am - 12pm on Wednesday Added lines 16-21:
'''''Announcements''''' Revised notes online below. (future changes will be kept minimal this semester). ---- Added line 26:
Deleted lines 27-32:
'''''Announcements''''' Revised notes online above. (future changes will be kept minimal this semester). ---- Changed line 36 from:
from the revised course notes. to:
from the revised course notes. Changed line 4 from:
%thumb width=700px% Attach:2lvlAt. to:
%thumb width=700px% Attach:2lvlAt.png | [- Two level atom coupled to a single mode of the Electromagnetic field. -] Changed line 4 from:
%thumb width=700px% Attach:2lvlAt. to:
%thumb width=700px% Attach:2lvlAt.pdf | [- Two level atom coupled to a single mode of the Electromagnetic field. -] Changed lines 3-4 from:
>>rframe width= %thumb width= to:
>>rframe width=800px<< %thumb width=700px% Attach:2lvlAt.png | [- Two level atom coupled to a single mode of the Electromagnetic field. -] Changed lines 3-4 from:
>>rframe width= %thumb width= to:
>>rframe width=700px<< %thumb width=600px% Attach:2lvlAt.png | [- Two level atom coupled to a single mode of the Electromagnetic field. -] Changed line 4 from:
%thumb width=500px% Attach: to:
%thumb width=500px% Attach:2lvlAt.png | [- Two level atom coupled to a single mode of the Electromagnetic field. -] Changed lines 8-9 from:
''Prerequisites:'' PHSI 331 and 332. PHSI to:
''Prerequisites:'' PHSI 331 and 332. PHSI 336 strongly recommended. Deleted lines 13-18:
[[Attach:scheduleV1.pdf|Version 1 ]] [[Attach:scheduleV2.pdf|Version 2 ]] Deleted lines 15-30:
'''''I. Foundations''''' * Equations of motion, Symmetries and Conservation Laws * Pictures of quantum dynamics * Elementary quantum systems * The Density Operator * Second Quantization '''''II. Quantum Optics''''' * Quantum theory of the electromagnetic field * Fundamental processes in Quantum Optics * Dissipation in open quantum systems '''''II. Quantum Gases''''' * Scattering Theory * Degenerate Bose gases Changed lines 18-25 from:
[[Attach:AdvQII(405)_ [[Attach:AdvQII_M405_2014_V2.pdf|Version 2]] [[Attach:AdvQII_M405_2014_V3.pdf|Version 3]] [[Attach:AdvQII_M405_2014_V4.pdf|Version 4 to:
[[Attach:AdvQII(405)_2015_V1.pdf|Version 1]] Changed lines 24-29 from:
Exam revision advice - Monday 27th, 10am in G400. Note that this is Labour day, but we will still be able to get into the building - don't be deterred by tumbleweed blowing through the corridors of Physics. . to:
Revised notes online above. (future changes will be kept minimal this semester). Changed lines 30-61 from:
1. (a) Carry out the canonical quantization procedure for a simple pendulum consisting of mass m attached to a rigid massless rod of length L, that is fixed at the other end, and allowed to move in a single vertical plane. Take as your canonical coordinate the angle of the rod from vertical. (b) Give a ''qualitative'' account of the eigenfunctions of the Schroedinger equation by describing the limit of large and small energy (Hint: for this purpose you may ignore the fact that the angle is periodic and treat it as an unbounded coordinate). 2. Derive a recursion relation for the coherent states in the number state basis and use it to find the explicit expression for a coherent states given in the notes. 3. Show how the time ordering operator is used to reorder the Dyson series into exponential form. 4. Prove the Pauli matrix identities (e) and (f) of the notes. '''Assignment 2, (was) due Thursday 11/9/14. ''' Exercises 5.2, 5.6, 6.1, 7.5 '''EXTENSION:''' Now due on Wednesday 24/9/14 '''Assignment 3, due Friday 10/10/14. ''' Exercises 9.4, 10.7, 10.8 (version 3), equivalent to Exercises 9.6, 10.7, 10.8 (version 4) ---- to:
'''Assignment 1, due Wednesday August 12 ''' Problems 4.4, 4.5, 4.6, 5.1, 6.4 from the revised course notes. Changed lines 54-56 from:
Exam revision advice - Monday 27th, 10am in to:
Exam revision advice - Monday 27th, 10am in G400. Note that this is Labour day, but we will still be able to get into the building - don't be deterred by tumbleweed blowing through the corridors of Physics. .. Changed lines 58-59 from:
to:
Changed lines 73-74 from:
to:
Changed line 81 from:
to:
Added lines 53-54:
Exam revision advice - Monday 27th, 10am in G400 Changed line 52 from:
Last lecture today (10/10/2014), from to:
Last lecture today (10/10/2014), from 11am-1pm, in G400 Added lines 47-52:
---- '''''Announcements''''' Last lecture today (10/10/2014), from 11-1, in G400 Changed lines 73-74 from:
Exercises 9.4, 10.7, 10. to:
Exercises 9.4, 10.7, 10.8 (version 3), equivalent to Exercises 9.6, 10.7, 10.8 (version 4) Changed line 73 from:
Exercises 9.4 to:
Exercises 9.4, 10.7, 10.8 Changed line 73 from:
Exercises 9. to:
Exercises 9.4, 9.5, 10.7, 10.8 Added lines 68-75:
---- '''Assignment 3, due Friday 10/10/14. ''' Exercises 9.3, 10.8, 10.10 Changed lines 69-71 from:
---- '''Assignment 3, due ''' to:
---- Added lines 44-45:
[[Attach:AdvQII_M405_2014_V3.pdf|Version 3]] Changed lines 69-71 from:
---- to:
---- '''Assignment 3, due ''' Changed line 63 from:
Exercises 5.2, 5.6, 6.1, 7.5 to:
Exercises 5.2, 5.6, 6.1, 7.5 Changed lines 61-62 from:
'''Assignment 2, to:
'''Assignment 2, (was) due Thursday 11/9/14. ''' Changed line 65 from:
EXTENSION: Now due on Wednesday 24/9/14 to:
'''EXTENSION:''' Now due on Wednesday 24/9/14 Changed lines 61-62 from:
'''Assignment 2, due Thursday 11/9/14. ''' to:
'''Assignment 2, WAS due Thursday 11/9/14. ''' Changed line 2 from:
!Module 405: to:
!Module 405: Advanced Quantum Mechanics II (PHSI) Added lines 58-64:
---- '''Assignment 2, due Thursday 11/9/14. ''' Exercises 5.2, 5.6, 6.1, 7.5, 7.6 Changed line 42 from:
[[Attach: to:
[[Attach:AdvQII_M405_2014_V2.pdf|Version 2]] Changed line 42 from:
[[Attach:AdvQII405_2014_V2.pdf|Version to:
[[Attach:AdvQII405_2014_V2.pdf|Version 2]] Changed lines 17-18 from:
to:
[[Attach:scheduleV2.pdf|Version 2 ]] Added line 40:
[[Attach:AdvQII405_2014_V2.pdf|Version 1]] Changed line 27 from:
* to:
* Second Quantization Changed line 33 from:
* to:
* Scattering Theory Changed line 42 from:
'''Assignment 1 to:
'''Assignment 1, due Thursday 14/8/14. ''' Changed line 42 from:
'''Assignment 1''' to:
'''Assignment 1''', due Thursday 14/8/14. Added lines 12-19:
''Assessment:'' 30% assignments, 70% Exam (Closed book). ''''' Lecture schedule ''''' [[Attach:scheduleV1.pdf|Version 1 ]] ---- Deleted lines 34-41:
---- ''Assessment:'' 30% assignments, 70% Exam (Closed book). ''''' Lecture schedule ''''' [[Attach:scheduleV1.pdf|Version 1 ]] Added lines 28-29:
---- Changed lines 32-36 from:
to:
''''' Lecture schedule ''''' [[Attach:scheduleV1.pdf|Version 1 ]] ---- Changed lines 32-33 from:
[[Attach:AdvQII(405)_2014_V1.pdf| to:
'''''Lecture notes''''' [[Attach:AdvQII(405)_2014_V1.pdf|Version 1]] Changed line 32 from:
[[Attach:AdvQII_2014_V1.pdf|Lecture notes version 1]] to:
[[Attach:AdvQII(405)_2014_V1.pdf|Lecture notes version 1]] Changed line 32 from:
[[Attach:AdvQII.pdf|Lecture notes version 1]] to:
[[Attach:AdvQII_2014_V1.pdf|Lecture notes version 1]] Changed line 40 from:
2. Derive a recursion relation for the coherent states in the number state basis and to:
2. Derive a recursion relation for the coherent states in the number state basis and use it to find the explicit expression for a coherent states given in the notes. Changed lines 40-42 from:
2. 3. Derive a recursion relation for the coherent states in the number state to:
2. Derive a recursion relation for the coherent states in the number state basis and solve it to find an explicit expression for a coherent state in this basis. 3. Show how the time ordering operator is used to reorder the Dyson series into exponential form. Changed lines 36-38 from:
1. 2. ( to:
1. (a) Carry out the canonical quantization procedure for a simple pendulum consisting of mass m attached to a rigid massless rod of length L, that is fixed at the other end, and allowed to move in a single vertical plane. Take as your canonical coordinate the angle of the rod from vertical. (b) Give a ''qualitative'' account of the eigenfunctions of the Schroedinger equation by describing the limit of large and small energy (Hint: for this purpose you may ignore the fact that the angle is periodic and treat it as an unbounded coordinate). 2. Show how the time ordering operator is used to reorder the Dyson series into exponential form. Changed line 36 from:
1. Show how to reorder the Dyson series into exponential form. to:
1. Show how the time ordering operator is used to reorder the Dyson series into exponential form. Changed line 42 from:
4. to:
4. Prove the Pauli matrix identities (e) and (f) of the notes. Added lines 36-42:
1. Show how to reorder the Dyson series into exponential form. 2. (a) Carry out the canonical quantization procedure for a simple pendulum consisting of mass m attached to a rigid massless rod of length L, that is fixed at the other end, and allowed to move in a single vertical plane. Take as your canonical coordinate the angle of the rod from vertical. (b) Give a ''qualitative'' account of the eigenfunctions of the Schroedinger equation by describing the limit of large and small energy (Hint: for this purpose you may ignore the fact that the angle is periodic and treat it as an unbounded coordinate). 3. Derive a recursion relation for the coherent states in the number state basis and solve it to find an explicit expression for a coherent state in this basis. 4. Exercise 4.1 Deleted lines 11-14:
[[Attach:AdvQII.pdf|Lecture notes version 1]] Added lines 29-34:
[[Attach:scheduleV1.pdf|Lecture schedule version 1 ]] [[Attach:AdvQII.pdf|Lecture notes version 1]] '''Assignment 1''' Changed lines 24-25 from:
to:
'''''II. Quantum Optics''''' Added lines 28-29:
'''''II. Quantum Gases''''' * Second Quantization Changed line 31 from:
to:
Changed lines 2-3 from:
>>rframe width= %thumb width=500px% Attach:aqIIa.png | [- to:
>>rframe width=600px<< %thumb width=500px% Attach:aqIIa.png | [- Squeezing a minimum uncertainty state-] Changed line 3 from:
%thumb width=500px% Attach: to:
%thumb width=500px% Attach:aqIIa.png | [- -] Changed lines 2-3 from:
>>rframe width= %thumb width= to:
>>rframe width=500px<< %thumb width=500px% Attach:aqII.png | [- -] Changed line 3 from:
%thumb width= to:
%thumb width=400px% Attach:aqII.png | [- -] Changed lines 2-4 from:
to:
>>rframe width=350px<< %thumb width=300px% Attach:aqII.png | [- -] >><< Changed lines 5-6 from:
PHSI 331 and 332. PHSI 334 recommended. to:
''Prerequisites:'' PHSI 331 and 332. PHSI 334 recommended. Changed lines 5-6 from:
to:
!!!Prerequisites: PHSI 331 and 332. PHSI 334 recommended. Added lines 5-6:
''Prerequisites:'' PHSI 331 and 332. PHSI 334 recommended. Changed line 9 from:
'' to:
''Class rep 2014:'' Andrew Pauling Changed line 11 from:
[[Attach:AdvQII.pdf| to:
[[Attach:AdvQII.pdf|Lecture notes version 1]] Added line 5:
''Lecturer:'' Ashton Bradley. Room 416. Ph 4794121. ashton.bradley@otago.ac.nz Changed line 7 from:
[[Attach: to:
[[Attach:scheduleV1.pdf|Lecture schedule version 1 ]] Added lines 8-9:
[[Attach:AdvQII.pdf|Advanced Quantum II lecture notes]] Deleted line 4:
Added lines 6-7:
[[Attach:schedule.pdf|Lecture schedule version 1 ]] Changed line 23 from:
''Assessment:'' to:
''Assessment:'' 30% assignments, 70% Exam (Closed book). Changed line 1 from:
!Module 405: Advance Quantum Mechanics II to:
!Module 405: Advance Quantum Mechanics II (PHSI) Changed lines 1-3 from:
Module 405 (second semester). to:
!Module 405: Advance Quantum Mechanics II Changed line 1 from:
[++Advance Quantum Mechanics II++] to:
[++Module 405: Advance Quantum Mechanics II++] Changed line 10 from:
''''I. Foundations'''' to:
'''''I. Foundations''''' Changed line 17 from:
''''II. Applications'''' to:
'''''II. Applications''''' Changed line 10 from:
I. to:
''''I. Foundations'''' Changed line 17 from:
II. to:
''''II. Applications'''' Changed lines 1-3 from:
to:
[++Advance Quantum Mechanics II++] Module 405 (second semester). Changed lines 1-6 from:
Module 405 and the * Prerequisites: * Semester: 2 to:
Module 405 (second semester) deals with '''Advanced Quantum Mechanics II''':- This course presents a treatment of non-relativistic many-body theory with applications to quantum optics and degenerate quantum gases. ''Prerequisites:'' PHSI 331 and 332. PHSI 334 recommended. ''Subjects include:'' I. Foundations * Equations of motion, Symmetries and Conservation Laws * Pictures of quantum dynamics * Elementary quantum systems * The Density Operator * Scattering Theory * Second Quantization II. Applications * Quantum theory of the electromagnetic field * Fundamental processes in Quantum Optics * Dissipation in open quantum systems * Degenerate Bose gases * Degenerate Fermi gases and BCS theory Added lines 1-8:
Module 405 deals with '''Advanced Quantum Mechanics II''':- Quantum theory of the electromagnetic field; the density operator; quantum cryptography and the quantum computer; many body formalism; theory of the quantum gas; scattering theory. * Prerequisites: PHSI 331 and 332. PHSI 334 recommended. * Semester: 2 ---- |