SM358 exam debrief

As promised here is my summary (off the top of my head) of the questions and my responses to them
I think I'm on target for the top end of Grade 3 or if I'm lucky Grade 2 but it will only just get there.

The first part was 10 out of 12 questions of which I answered 9 but some were only sketches

Question 1 was about the degeneracies of energy levels in an infinite square well and the calculation of the wave length of light emitted when the electron fell from the higher level to the other.
Got most of this out 4  marks say

Question 2 Concerned the normalisation of of a given wave function and a calculation of the energy levels  again got most of this out 4 marks say

Question 3 I ignored think it involved calculation of quantum oscillator properties using annhilation and creation operators

Question 4 On the Born interpretation this had a different twist to the normal ones and threw me so I wrote down the born intepretation 1 mark out of 5

Question 6 Involved calculating the Energy eigenvalues of Lz for a given wave function then a question using the generalised uncertainty principle for Ly and Lx most out say 4 out of 5

Question 7 Involved calculation of the maximum separation of proton distance from a given radial wavefunction got most of this out again say 4 out of 5

Question 8 was fairly straightforward whether or not statements about the Bell Inequalities were true or false I think I got most of theses so 4 marks

I can't really remember most of the other questions in part 1 but they involved calculation of the expectation value of various quantites such as x or x^2. The calculation of bond order for a given molecular configuration and so forth. If my memory serves me correctly I got about 4 marks for two and say 2 marks for the other one
So pessimistically total marks for part 1 
so overall for part 1 I got 4+4+1+4+4+4+8+2 = 31 marks (Some may include full marks so possibly 35 marks )

Then parts 2,3 and 4 long questions

Part 2 I chose a question on eigenfunctions of a square well I think I got most of this so say 15/17

Part 3 was a question on spin functions the first part was really strange so I left it.losing 3 marks went onto the question in part 4 before coming to this question at the end..
  The rest should have been quite straightforward as it involved  calculating the coefficients of a given spinor in another basis and then the expectation value of Sy. I got the  first part out but chose the wrong matrix to calculate the expectation value. I might just scrape 8 or nine marks here

Part 4 was a question on eigenfunctions of the angular momentum operator in spherical coordinates
Got most of the first part out but then there were two part questions on of which involved showing a given wave function was an eigenfunction of J = Lz + Sz I couldn't quite get this. The last part should have been straightforward involving transition selection rules but my mind went blank so possibly 12 out of 17 here.

So part two is about 35 marks as well

35 + 35 is 70 so might just get grade 2 but a more realistic assessment would be for grade 3.

So overall not bad (certainly better than last june's car crash of Fluid mechanics) I decided not to do the resit as it clashed with my revision for quantum mechanics.

Number theory and logic awaits and I want to consolidate my music by doing the Grade theory exams I should be able to do Grade 5 in March and also piano lessons again I want to do grade 1 piano again in March. I will also get back to my own physics calculations. My first project is to examine the X ray diffraction theory behind the discovery of DNA. Then back to general relativity and also the physics of deep inelastic scattering which lead to the discovery of quarks. I will also do an Edinburgh dept continuing education course on Plato come January Enough to keep me busy for a while yet :)

Bye for now
 

Exam Time again

Well it's that time of year again for me (twice in one year) I have my quantum mechanics exam on Monday
I did my first practice past paper under exam conditions today and got borderline grade3/grade2 part of the problem is there is just not enough time available. For part 1 you have to answer 10 so called short questions in 1 hour and 30 minutes and then there are three long questions which you are supposed to allocate 30 mins to. This means that you almost have to download the already prepared answers in your head if you are to stand any chance of a grade 2.

The short questions seem to range over a variety of topics whereas the long questions can be grouped into 3 quite distinct groups

PArt 1 A question on a particle in a potential usually square but sometimes they will throw a wobbly and ask about a non square potential or just some general type questions. This is a banker question

Then there appears to be a choice between a question involving Transmission or reflection at a boundary or one on Harmonic oscillator raising and lowering operators. Will hope the question on potential is reasonable

Part 2 A question on spin states in a magnetic field again a banker question the alternative is usually a question on the Bell inequalities

Part 3 A question on hydrogen atom wave functions which could get messy however it's a topic I feel reasonably confident in although in my trial I couldn't for the life of me see how to get the normalisation of a given hydrogen atom wave function correct.

The second question is usually on something involving molecules, solid state physics, perturbation theory or Transistions induced by radiation. I've not paid much attention to this part which comes at the end of the course so I'll go for the question on Hydrogen atom wavefunctions. If it looks really tough then if a question on perturbation theory comes up I'm reasonably confident I could tackle that one.

In part 1 typical questions include normalising a wave function via the coefficient rule. Calculating a probability density function from Born's rule. A bit on hermitian operators, one or two questions on the Bell Inequalities and spin states, Then a whole bunch of questions on either molecular or atomic orbitals
Selection rules between states induced by radiation one or two waffly questions on solid state physics and so forth

Ok prediction top end of grade 3 or if I'm lucky grade 2

On another note I've got the material for Number Theory and Logic which has officially started  but so far apart from a quick glance I've not had any chance to look at it. The first unit looks reasonably straightforward covering Triangular numbers, Induction and Divisibilty some of which was covered in the last unit of MST221 so hopefully I will be able to get up to speed,

Post match analysis on Tuesday till then that's all folks

SM358 quantum physics TMA04

So final TMA submitted for SM358 but still have 3 on line assessments to complete one nearly finished and of course I missed out on TMA02 as was bogged down in completing the EMA for the music course and desperately attempting to do revision for Fluids

TMA04 concentrates on the first part of the 3rd block quantum mechanics of matter this involves an overview of the hydrogen atom and it's wave functions, and it's extension to many electron atoms plus an introduction to pertirbation theory. The rest of the unit is (IMHO) a rather inadequate introdution to molecular physics, Solid state physics and quantum optics. Each of these deserve at least a 30 point unit to themselves and again I feel the OU is selling it's physics graduates short. Anyone thinking that by completion of this course, electromagnetism and say the relativistic universe has a degree equivalent to that of a standard course in undergraduate physics would be kidding themselves. Still I don't write the rules and it is not the point of this post to beef (yet again ) about the gulf between OU courses and those of brick univesities.

So the questions on this TMA divided into 3

1) A question based on one particular wave function of the hydrogen atom, calculating various quantities such as the expection value of 1/r and 1/r^2 and their uncertainty. As they say in the books this was tedious but straightforward

2) Again more questions on the hydrogen atom wave functions involving a hypothesised modification to the coulombic interaction. In the context of the hydrogen atom this is obviously unphysical however it may correspond to the force between two nucleons such as the potential between two deuterons. Any way the point was to test our ability to calculate the first order corrections to a change in the potential. Again this was straightforward but tedious and it took a couple of goes before all the signs and factors of pi cancelled out to get the correct answer.

One of the skills one needs in solving problems concerning hydrogen atom wavefunctions is patience and the ability to obtain the correct numerical factor. This is somewhat tedious but a necessary skill just hope the exam questions aren't so pernickity and fiddly.

3) The final question probably the most straightforward involved calculation of the various atomic terms associated with a multi electron atom and their degenaricies. Just one point that wasn't really mentioned in the text namely how to correlate the total number of States given with a given L and S nuimber with the individual l and s numbers of the valence electrons. Fortunately an example in the additional exercise book gave a clue

So all in all I think I've done reasonably well on this TMA. I omitted an essay type question at the start of question 3.

So that apart from completing the exam and the online assessments is that as far as quantum mechanics goes. It really doesn't seem all that long ago since I started and now it's more or less finished the feeling does seem a bit weird to say the least but the same is true of any OU course. It is just rather a pity to say the least that there are no follow up courses as far as the OU is concerned.

Statisical and Solid State Physics

Well it's nearly the end of SM358 unfortunately the open university has no where else to go as far as quantum physics is concerned. A next logical step is Statistical Physics and Solid State Physics A search through the internet has yielded these two courses which seem to give a good over view of the subject and are based on courses given to those in their third year at Oxford and Cambridge whats more they have problem sheets associated with them


Statistical Physics

http://www.damtp.cam.ac.uk/user/tong/statphys.html

Solid State Physics

http://www-thphys.physics.ox.ac.uk/people/SteveSimon/condmat2013/condmat.html

If any one is interested in forming a study group to work through these courses after the exams could they please let me know. Obviously we would have to share any solutions amongst our selves as if they were published on the internet then the authors might well restrict access to the lecture notes.

Two suitable textbooks to accompany both might be

http://www.amazon.co.uk/Concepts-Thermal-Physics-Stephen-Blundell/dp/0199562105

and by the author of the solid state course himself (and honour would suggest the least we could do is buy his book)

http://www.amazon.co.uk/Oxford-Solid-State-Basics/dp/0199680779/ref=sr_1_1?s=books&ie=UTF8&qid=1376838763&sr=1-1&keywords=Simon+Solid+State+physics

I have also been looking at the diffraction theory behind the discovery of DNA it really is quite clever and I hope to write up a paper which covers the theory and goes through the actual calculations. Watch this space

Coursera

Ok so there is an alternative to the OU which I’m going to use to supplement my current OU studies. I’m sure most people reading this blog will have heard of Coursera which is a free on-line set of courses provided by mainly American Universities. It’s like being a kid in a sweet shop. The courses are short.

I’m doing a) Mathematical Philosophy whiich started last week and I’m grateful for Gavin who pointed this out to me in a comment he made on the last post

https://class.coursera.org/mathphil-001/wiki/view?page=syllabus

b) Introduction to Logic which starts in September and should hopefully complement the Logic part of M381 https://www.coursera.org/#course/intrologic?utm_classid=971129&utm_nottype=class.welcome.before&utm_notid=-1&utm_linknum=1

c) Finally (for now) Analysis of a Complex Kind which starts end of October this hopefully will remind me about complex analysis and help me revise the topic

https://www.coursera.org/#course/complexanalysis?utm_classid=971056&utm_nottype=class.welcome.before&utm_notid=-1&utm_linknum=1

 It might also be a good introduction for those who are contemplating doing M337 next year

I really am begining to think the OU days are numbered for those who want to do courses mainly for interest given the cost of fees.Ok one gets more support but as Free internet provision of University level courses continues to grow it's difficult to see how the OU can justify it's expensive fee structure.

Incidentally I've just had a hell of a nightmare trying to publish this post I was using Internet Explorer 8 however blogger in their infinite wisdom have decided to withdraw support from Internet Explorer 8 so I've had to change to FireFox a case of if it's working we'll break it. Most inconvenient and tedious. Also in order to access the Coursera courses I had to download VLC media and access the videos that way but that came with a whole load of crap such as sweetsearch so I had to remove these manually. I hate computers.

Results out

Just a quick post to inform readers that my results are out

I got grade 3 for music with 61% OCAS (TMA's not bad since I only submitted 5 out of 6 ( and there is no substitution ) and 65% for the EMA (Extended Module Assessment) so reasonable there is as yet no feedback for the EMA but it's forthcoming

As for Fluids I failed with 37% for the exam and 71% for the continuous assessment I've been offered a resit but it will be capped most I can get is grade 4 .
Still as I would like the opportunity to hone my exam technique and reconsolidate the material  it will be worth doing. Also it's another excuse to keep up with partial differenctial equations and mathematical methods.

My course schedule for this year is

SM358 Quatum mechanics exam in October
M381 logic and number theory starting in October
Physics project on entanglement Feb 2014

Also for music
I will enrol for grade 4 theory exam in November with a theory exam every 6 months or so till I get to grade 8 start piano lessons in September and hopefully do grade 1 piano exams in March 2014

I decided it would be far to much for me to take on board AA308 the third level course in philosophy this year round. It's allegedly in it's last presentation this year with a replacement in Oct2014 but going on previous form I can't see this happening so hopefully it will be available in October   I really hope so as from a preliminary survey I don't really like the prospectus for the new course without being to harsh it fits into "waffle philosophy".That is  philosophy good for discussion at dinner parties but hardly cutting edge philosophy that one would expect for a third level course in the subject. On the other hand AA308 whilst not perfect does cover philosophy of the mind at a level comparable to that of other 3rd year undergraduate brick level courses.

I am seriously begining to think the only way in which to get  a rigorous training in philosophy is to bite the bullet and do the external London BA in philosophy even though I wont be able to start for another two years.  Watch this space.

SM358 quantum mechanics TMA03

Ok so back to quantum mechanics I have just submitted the third TMA and am reasonably confident I've done enough to get a grade two pass not that this matters for the assessment as one only needs above 30% in seven of the assessments of which at least two must be TMA's. Due to the intensity of revising for both my music course and fluid mechanics I was unable to complete the second TMA but will look at it for the exam.

Anyway a breakdown of the TMA questions is as follows

1) A question on the time dependence of spin states the basic theory of which under pins magnetic resonance imaging. One had to calculate how a composite spinor would vary with time the expectation values of the Sx and Sy spin components and check that the results were consistent with the generalised Ehrenfest theorem I got consistent answers so am reasonably confident I got most of this correct.

2) A question involving the symmetries of a system of two particles in a square well. Given a spin state one with a given Spin quantum number S one had to determine the symmetry of the spatial wavefunction. So if the spin state is zero say for a pair of fermions with a wavefunction that is asymmetric if  the spin part is antisymmetric, the spatial part of the wavefunction must be symmetric to maintain the overall antisymmetry of the wave function. This was again relatively straightforward although one had to calculate the probability that both particles would be in the left hand side of the box from the joint wavefunction and this was quite tedious also causing word to crash a number of times as the equation editor can't handle to much copying of equaitons without it crashing. Always remember to save the document after writing complicated equations.

3) A question on the polarisation states of a pair of photons and a gentle run through of the steps leading to the violation of the Bell inequalities or in our case to be more precise the Clauser Horne Shimony (CHSH) inequalities. Plus a short description of what a non local hidden variable theory was. All this was straightforward  and satisfying. Although I do feel that the way the text has phrased the two conditions of realism and non realism slightly misleading to say the least

It defines the features of a local hidden variable theory as follows

a) Realism implies that observables have values independent of meausrement

With of course the implication that if the so called collapse of the wavefunction is seen as a physical process observables in quantum mechanics are not independent of measurement. That is not strictly true its only non commuting variables that on the standard view do no have values independent of measurement. Quantities such as mass and charge are commutative and so do have values of measurement. Also if as I have argued in many posts before the wavefunction is just a means for calculating the correct probabilities and nothing physical then nothing can be said to collapse.

b) Locality implies that events at any location cannot influence what happens at another location before a light signal could travel between the two locations

This is of course the standard view with the implication that in situations such as the Aspect experiment when a measurement is made on one photon it causes the other photon to jump into the opposite spin state even though they may be miles away thus implying some faster than speed of light influence between the particles.
Of course the formalism of quantum mechanics says nothing about what might be causing the correlation but that hasn't stopped all sorts of weird and wonderful ideas about it.

A more prosaic view would say that non locality is essentially the fact that the probability distributiion function for a joint pair of variables is non separable whereas for local theories they are. All that happens in the Aspect experiment is that because the pair of particles have to have a net angular momentum of zero and this dicatates the form of the wavefunction for the joint pair of particles leading to the correlation. But no more can be said certainly there is no need to invoke faster than light signalling as some people are prone to. That is an addition to the formalism not warranted by the facts.

Finally whilst it's true to say that local hidden variable theories have been refuted the current form of hidden variable theories are in fact non local. The issue is still wide open, What one can't have is the usual view that quantum mechanics is both non realist and non local. If you claim that quantum mechaincs is non realist with respect to non commuting variables then there is no need to claim that  quantum mechanics is non local. And also the non realism associated with quantum mechanics is only a limited form of non realism.

I didn't have the space to go into this in any detail in the assignment. It does concern me slighthly that misleading interpretations are being passed of as fact when in fact the situation is not as black and white as some people make out. Watch this space for when I embark on the entanglement project.