Tuesday, 8 October 2013

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

Thursday, 3 October 2013

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