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29 Mar 2021: integral as. n 4. (2)3 eµ. Z 1. 0. dp p2ep2/2m =. mkBT. 22. 3/2eµ (2.24). Let’s try to interpret this. Read naively, it seems to tell ... anti-aligned to give 3 dierent spin 1 states. With these two amendments, our expression for the number density (2

16 Apr 2021: D : (3 ττ ) kiki , (4.24)b K : (3 ττ ) 2biki b kkiki 2kikibjkj. ... R|comoving R =A. 2. (5.24). The metric then takes the form.

8 Jul 2021: Received 13 May 2020; revised 18 February 2021; accepted 24 February 2021). ... Ω. , (2.23). where. A = 6ζ‖ 4Δζ (φ21 φ22 ) O(φ4), (2.24)B = 4Δζ (φ1 φ2) 83 Δζ (φ31 φ32 ) O(φ4), (2.25).

8 Oct 2021: hx| i =Z. R (x0) hx|x0i dx0 = (x). (2.24). In other words, the position space wavefunctions we’re familiar with are nothing but the.

25 Aug 2021: 1.2.2 The Scattering Amplitude 22. 1.2.3 Partial Waves 24. 1.2.4 The Optical Theorem 27. ... r(1.24). The 1/r fall-off follows from solving the free Schrödinger equation; we’ll see this ex-.

18 Oct 2021: ρ. =. e. -. β. H. Z. (1.24). If we make a measurement described by an operator. ... In the quantum context, it is sometimes written in terms of the density matrix (1.24) as.

18 Oct 2021: and. -. 𝑑. x. x. e. -. a. x. 2. =. 0. (2.24). where the second equality follows because the integrand is odd (and suitably well behaved at infinity). ... σ. ). exp. (. -. x. 2. σ. |. α. |. 2. ). =. k. 0. where, to get the final equality, we did the

18 Oct 2021: v. r. (. p. ). Figure 23: An incoming anti-fermion. Figure 24: An outgoing anti-fermion. •.

18 Oct 2021: 3 Quantum Gases. 3 Quantum Gases. In this section we will discuss situations where quantum effects are important. We’ll still restrict attention to gases — meaning a bunch of particles moving around and barely interacting — but one of the

10 Sep 2021: Active Brownian motion tunable by light. J. Phys. Condens. Matter 24, 284129 (2012). ... Soft Matter 16, 4961–4968 (2020). 24. Shao, J. et al. Erythrocyte membrane modified Janus polymeric motors for thrombus therapy.