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The equation for spherical harmonics is not in the formula sheet. Are we expected to memorise this, or will any questions in the exam give us the value for the Spherical Harmonic?

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What is the relation between m(l) and m(j) because I've seen solutions which add m and m(s) to get m(j) where as m(l) seems like it would require a subtraction?

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Should the lambda square term not have a negative sign in front of it since two complex numbers have been multiplied to get it?

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What commutation rules have been used to get the first expression on the 3rd line, the order of some of the momentum and spacial operators seem to have been switched? Also, should the first term on the 2nd line not be y p(z) z p(x) instead of y p(z) z p(z)?

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What is meant by classical turning points\ What section of the notes covers this?

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Where has the expression for E+V0 come from?

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The section in the notes that covers delta potentials seem to give l^2 =-2m(E-V)/h^2. Is there any reason why the minus sign is not included in this example? Also wondering the A and C terms have negative potential when they are normally positive for the positive x direction?

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How has the second line been reduced to the third line? I'm struggling to find expressions for the L^2 and L^2x operators that simplify to give this result.

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I'm a bit confused about what fractions they are using in this solution, are they squaring the c11 probability from part (iii) to give the total fraction?

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How is the bracket in the left hand expression and the whole of the right hand expression obtained from the equation given in the question? The left hand side seems to square root the coefficient of x^2 and the right hand side squares it?

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Is there any difference between bound and stationary states?

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Why in the 2021 past paper, in question 2aii, does the incoming wave get represented with a negative in the exponent and the reflected wave does not? In the question, it tells us that the beam is travelling in the +x direction, so surely it makes more logical sense to have the wave function S(x) = Ae^(ika) + Be^(-ika)? Where A is the amplitude of the incoming wave and B is that of the reflected wave.

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Gaussian wavepackets and the heiseberg UP

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Gaussian wavepackets and the heiseberg UP

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I get that it states in the notes for the Gaussian wavepacket undergoing FT it would be proportional to 1/roota, but how can we just switched this from the 1/2pi to this without changing anything? Also, what are the sigmas here actually representing, are they based on the factor of a in exponent?

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How does this expansion of the commutator work? Are there specific rules or do you just have to do the algebra to work it out? Also is the first term negative because of the ordering of x&z?

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I'm not sure where this line of working has come from. How have we rearranged px this way?

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Is there a reason we take g=2 here?

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Defining eigenvalues?, question sheet 4 Q7

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Defining eigenvalues?, question sheet 4 Q7

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I'm slightly confused about what the chi symbols are representing here? It was my understanding that the lambdas are the eigenvalues? So I'm wondering what the chi symbols represent and how they are found.

Thank you

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Does the first term go to zero because the ladder operator changes the m quantum number to 1+1, and then because the inner product of spherical harmonics with different m quantum numbers goes to zero, like in the second term? Or is it to do with the allowed range for m being -l<m<l, so the ladder operator acts against the rules of this makes it go to zero? Or a completely different reason? Thanks

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Is there an equation missing from the formula sheet?

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Is there an equation missing from the formula sheet?

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Under "Time evolution and Shrodinger Equation" there's a space left after "time evolution:". Wondered if there was meant to be a formula here.

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What is meant by “local/non-local” physics, first mentioned in the EPR paradox slide?

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Is the material in slideshow 9 examinable? It isn't covered in the mini-summary

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What is the general form of a Gaussian wave function?

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Why do the ky and kz terms have a 1/a factor instead of having factors of 1/b and 1/c respectively?

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How do you find the possible results of a measurement taken on a system? For example, question 10 of exercise sheet 2. It is not very clear in the solutions where anything comes form.

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How do you find the possible results of a measurement taken on a system? For example, question 10 of exercise sheet 2. It is not very clear in the solutions where anything comes form.

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on powerpoint 2, slide 18. how does the previous line make this?

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Apologies for the silly question, but I was doing Q6 of problem sheet 1, and when taking the square integral normalisation, the denominator of the exponent loses the 2, and I'm slightly unsure as to the maths that allows us to do that. Thanks in advance

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When will the solutions to problem sheet 2 be made available please?

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On slide 4 of ppt 6 covering the infinite square well, we get this as a result for the energies, but where does this equation derive from?

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Would you be able to tell us in which order you cover the book chapters? Thanks!

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what decides the direction operators work in?

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what decides the direction operators work in?

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Are uppercase psi 𝚿 and lowercase psi ψ interchangeable as the symbol for a wavefunction? The slides and the course summary seem to use different symbols in the same equations

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When will the answers to the problem sheets be released

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I can follow the derivation up until this point, and maybe its just sleep deprivation, but how does the 2x4pi x 1/8 = 8pi?

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In lecture 3, we derived and talked about the dispersion relation of newtonian dynamics, light, and relativity.

I think I understand that the newtonian and relativity ones are just energy conservation for each, but why do we define the light dispersion the way we do? Thanks :)

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I'm having some trouble following the way we've defined the fourier transform, as when we convert from k-space to x-space, there is also an e^(i omega t) factor in the integral, which I am only used to seeing when we convert from a frequency space function. Having both k and omega at the same time doesn't seem to fit the FT equation I know. Are we assuming that f(x) actually holds a composite variable, for example f(x-vt), to make this work?

Then in the slide on conservation of probability, f becomes a function of two variables f(x,t), and is generated from the transform of g(k, 0). If we transform a two variable function, don't we need a double integral? Also why are we allowed to set t=0 in the k-space function?

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Is there any chance lecture slides could be posted a lecture in advance please?

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Where can the lecture recordings for this course be found?