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31 May 2024: entries is independent of the choice of basis. (This theorem has nothing to do with. ... all diagonal entries of the metric are positive. A manifold equipped with such a metric.

26 Jun 2024: function with itself is positive definite. In fact, our normalisability requirement (3.1). ... The requirement that the wavefunctions are single valued functions then tells us that.

12 Jun 2024: Why don’t. we just do something much simpler and multiply entries together component by compo-. ... is because it’s only there that the ijk symbol has three entries.

2 Jul 2024: AB. We will not impose any such requirements if [A, B] 6= 0. ... In this case, the requirements of the Kocken-Specker theorem tell us that one of these.

31 May 2024: This conceptleads us to our final requirement: we require that, given any two distinct points, there. ... To do this, simply replace one of T. p(M) entries with a basis vector.

2 Jul 2024: This is a strong requirement. First, it relates the absorption and stimulated emission coecients. ... g1B12 = g2B21 (4.29). We see that, as promised, it is a thermodynamic requirement that stimulated emission.

26 Jun 2024: requirement that the wavefunction should be periodic, so that. ψ(x 2πR) = ψ(x). ... Not all solutions (2.5) obey this requirement. We must have. eik(x2πR) = eikx e2πikR = 1.

31 May 2024: the requirement that no signal can travel faster than light. Our goal is to figure out.

2 Jul 2024: ΘeiHt/ |ψ(0)⟩ = eiHt/ Θ |ψ(0)⟩. Expanding this out for infinitesimal time t, we get the requirement. ... the adjoint A† is defined by the requirement. ⟨ϕ|A†|ψ⟩ = ⟨ψ|A|ϕ⟩.

12 Jun 2024: with the additional requirement of z = 0 prompting the artistic flourish that results in. ... Implicit in our previous proof was. the requirement that we have a continuous function ϕ, well defined everywhere on R2.Strictly speaking, a conservative field

26 Jun 2024: and this is where the quantisation requirement now comes from. In fact, we have seen. ... Yang-Mills. On a spacetime manifold S3 (or on R3 with the requirement that gauge.

26 Jun 2024: go down this path, we must solve the = 0 Schrödinger equation with the requirement. ... to worry about; instead, it’s simply the requirement that the wavefunction is single.

31 May 2024: mediating quantum mechanical tunnelling events. The requirement of finite action means that the potential Aµ must become pure. ... chiral (0,4) theory, where the two entries correspond to left and right moving fermions.

3 Jul 2024: Together with. the requirement that the transformation is linear, this restricts. ... But this is. something that we’ve seen before: it is the requirement for R to be a rotation matrix.

11 Jun 2024: A requirement of FEM meshes is that they are not ‘tangled’,i.e.

3 Jul 2024: Preprint typeset in JHEP style - HYPER VERSION Lent Term, 2013. Dynamics and RelativityUniversity of Cambridge Part IA Mathematical Tripos. David Tong. Department of Applied Mathematics and Theoretical Physics,. Centre for Mathematical Sciences,.

12 Apr 2024: Preprint typeset in JHEP style - HYPER VERSION Michaelmas Term, 2017. Statistical Field TheoryUniversity of Cambridge Part III Mathematical Tripos. David Tong. Department of Applied Mathematics and Theoretical Physics,. Centre for Mathematical

27 Apr 2024: Lent Term, 2015. ElectromagnetismUniversity of Cambridge Mathematical Tripos. David Tong. Department of Applied Mathematics and Theoretical Physics,. Centre for Mathematical Sciences,. Wilberforce Road,. Cambridge, CB3 OBA, UK.

26 Jun 2024: Preprint typeset in JHEP style - HYPER VERSION Michaelmas Term, 2019. CosmologyUniversity of Cambridge Part II Mathematical Tripos. David Tong. Department of Applied Mathematics and Theoretical Physics,. Centre for Mathematical Sciences,.

2 Jul 2024: E2)n,j;l = Ze22. 4.40(mc)2. ((l 1). l. )1. r3. n,j;l. where, as in (3.13), the upper entry in {} corresponds to j = l ... the lower entry corresponds to j = l 12. Note that when l = 0, we have E2 = 0.