diff options
Diffstat (limited to 'content/know')
25 files changed, 151 insertions, 2 deletions
diff --git a/content/know/concept/bell-state/index.pdc b/content/know/concept/bell-state/index.pdc index 5e147e2..9fe69d1 100644 --- a/content/know/concept/bell-state/index.pdc +++ b/content/know/concept/bell-state/index.pdc @@ -91,3 +91,9 @@ then $B$ instantly also collapses into $\ket{0}$, never $\ket{1}$, even if it was not measured. This was a specific example for $\ket*{\Phi^{+}}$, but analogous results can be found for the other Bell states. + + +## References +1. J.B. Brask, + *Quantum information: lecture notes*, + 2021, unpublished. diff --git a/content/know/concept/calculus-of-variations/index.pdc b/content/know/concept/calculus-of-variations/index.pdc index 576863c..a8861cb 100644 --- a/content/know/concept/calculus-of-variations/index.pdc +++ b/content/know/concept/calculus-of-variations/index.pdc @@ -338,3 +338,6 @@ And then the remaining $N - M$ equations can be solved in the normal unconstrain 1. G.B. Arfken, H.J. Weber, *Mathematical methods for physicists*, 6th edition, 2005, Elsevier. +2. O. Bang, + *Applied mathematics for physicists: lecture notes*, 2019, + unpublished. diff --git a/content/know/concept/convolution-theorem/index.pdc b/content/know/concept/convolution-theorem/index.pdc index 86543d8..9d1a666 100644 --- a/content/know/concept/convolution-theorem/index.pdc +++ b/content/know/concept/convolution-theorem/index.pdc @@ -98,3 +98,10 @@ $$\begin{aligned} &= \int_0^\infty \tilde{f}(s) g(t') \exp(- s t') \dd{t'} = \tilde{f}(s) \: \tilde{g}(s) \end{aligned}$$ + + + +## References +1. O. Bang, + *Applied mathematics for physicists: lecture notes*, 2019, + unpublished. diff --git a/content/know/concept/density-of-states/index.pdc b/content/know/concept/density-of-states/index.pdc index 195ac2a..438a0d6 100644 --- a/content/know/concept/density-of-states/index.pdc +++ b/content/know/concept/density-of-states/index.pdc @@ -154,3 +154,6 @@ so a finite value can be chosen. 1. H. Gould, J. Tobochnik, *Statistical and thermal physics*, 2nd edition, Princeton. +2. B. Van Zeghbroeck, + [Principles of semiconductor devices](https://ecee.colorado.edu/~bart/book/book/chapter2/ch2_4.htm), 2011, + University of Colorado. diff --git a/content/know/concept/diffie-hellman-key-exchange/index.pdc b/content/know/concept/diffie-hellman-key-exchange/index.pdc index c0af364..7897e25 100644 --- a/content/know/concept/diffie-hellman-key-exchange/index.pdc +++ b/content/know/concept/diffie-hellman-key-exchange/index.pdc @@ -72,3 +72,10 @@ However, for quantum computers, it has already been *dis*proven! In this case, another method must be used, for example the [BB84 protocol](/know/concept/bb84-protocol/). + + + +## References +1. J.B. Brask, + *Quantum information: lecture notes*, + 2021, unpublished. diff --git a/content/know/concept/dirac-delta-function/index.pdc b/content/know/concept/dirac-delta-function/index.pdc index 97704d7..76b6e97 100644 --- a/content/know/concept/dirac-delta-function/index.pdc +++ b/content/know/concept/dirac-delta-function/index.pdc @@ -109,3 +109,10 @@ $$\begin{aligned} \int f(\xi) \: \dv[n]{\delta(x - \xi)}{x} \dd{\xi} = \dv[n]{f(x)}{x} } \end{aligned}$$ + + + +## References +1. O. Bang, + *Applied mathematics for physicists: lecture notes*, 2019, + unpublished. diff --git a/content/know/concept/dirac-notation/index.pdc b/content/know/concept/dirac-notation/index.pdc index 999c90c..176f769 100644 --- a/content/know/concept/dirac-notation/index.pdc +++ b/content/know/concept/dirac-notation/index.pdc @@ -127,3 +127,10 @@ $$\begin{aligned} \\ &= \braket{u}{f} \braket{g}{w} \end{aligned}$$ + + + +## References +1. R. Shankar, + *Principles of quantum mechanics*, 2nd edition, + Springer. diff --git a/content/know/concept/dispersive-broadening/index.pdc b/content/know/concept/dispersive-broadening/index.pdc index f053eb6..cae856d 100644 --- a/content/know/concept/dispersive-broadening/index.pdc +++ b/content/know/concept/dispersive-broadening/index.pdc @@ -93,3 +93,10 @@ Of great importance is the sign of $\beta_2$: in the **anomalous dispersion regime** ($\beta_2 < 0$), lower frequencies travel more slowly than higher ones, and vice versa in the **normal dispersion regime** ($\beta_2 > 0$). + + + +## References +1. O. Bang, + *Numerical methods in photonics: lecture notes*, 2019, + unpublished. diff --git a/content/know/concept/fourier-transform/index.pdc b/content/know/concept/fourier-transform/index.pdc index 96653f5..3be47ff 100644 --- a/content/know/concept/fourier-transform/index.pdc +++ b/content/know/concept/fourier-transform/index.pdc @@ -116,3 +116,10 @@ $$\begin{aligned} = \hat{\mathcal{F}}\{ (i s x)^n f(x) \} } \end{aligned}$$ + + + +## References +1. O. Bang, + *Applied mathematics for physicists: lecture notes*, 2019, + unpublished. diff --git a/content/know/concept/gram-schmidt-method/index.pdc b/content/know/concept/gram-schmidt-method/index.pdc index 0b02eee..97362e0 100644 --- a/content/know/concept/gram-schmidt-method/index.pdc +++ b/content/know/concept/gram-schmidt-method/index.pdc @@ -46,3 +46,10 @@ turns them into an orthonormal set $\ket*{n_1}, \ket*{n_2}, ...$ as follows: 4. Loop back to step 2, taking the next vector $\ket*{V_{j+1}}$. If you are unfamiliar with this notation, take a look at [Dirac notation](/know/concept/dirac-notation/). + + + +## References +1. R. Shankar, + *Principles of quantum mechanics*, 2nd edition, + Springer. diff --git a/content/know/concept/impulse-response/index.pdc b/content/know/concept/impulse-response/index.pdc index 012a2c3..b055fe7 100644 --- a/content/know/concept/impulse-response/index.pdc +++ b/content/know/concept/impulse-response/index.pdc @@ -62,3 +62,10 @@ $$\begin{aligned} \end{aligned}$$ *__Q.E.D.__* + + + +## References +1. O. Bang, + *Applied mathematics for physicists: lecture notes*, 2019, + unpublished. diff --git a/content/know/concept/kramers-kronig-relations/index.pdc b/content/know/concept/kramers-kronig-relations/index.pdc index 1d29f96..9b67d60 100644 --- a/content/know/concept/kramers-kronig-relations/index.pdc +++ b/content/know/concept/kramers-kronig-relations/index.pdc @@ -132,3 +132,10 @@ $$\begin{aligned} \end{aligned}$$ To reiterate: this version is only valid if $\chi(t)$ is real in the time domain. + + + +## References +1. M. Wubs, + *Optical properties of solids: Kramers-Kronig relations*, 2013, + unpublished. diff --git a/content/know/concept/lagrange-multiplier/index.pdc b/content/know/concept/lagrange-multiplier/index.pdc index fc1319e..7476dca 100644 --- a/content/know/concept/lagrange-multiplier/index.pdc +++ b/content/know/concept/lagrange-multiplier/index.pdc @@ -122,3 +122,6 @@ $$\begin{aligned} 1. G.B. Arfken, H.J. Weber, *Mathematical methods for physicists*, 6th edition, 2005, Elsevier. +2. O. Bang, + *Applied mathematics for physicists: lecture notes*, 2019, + unpublished. diff --git a/content/know/concept/legendre-transform/index.pdc b/content/know/concept/legendre-transform/index.pdc index 8a0d3e3..290a89a 100644 --- a/content/know/concept/legendre-transform/index.pdc +++ b/content/know/concept/legendre-transform/index.pdc @@ -87,3 +87,10 @@ $$\begin{aligned} Legendre transformation is important in physics, since it connects Lagrangian and Hamiltonian mechanics to each other. It is also used to convert between thermodynamic potentials. + + + +## References +1. H. Gould, J. Tobochnik, + *Statistical and thermal physics*, 2nd edition, + Princeton. diff --git a/content/know/concept/modulational-instability/index.pdc b/content/know/concept/modulational-instability/index.pdc index 26d2552..6856941 100644 --- a/content/know/concept/modulational-instability/index.pdc +++ b/content/know/concept/modulational-instability/index.pdc @@ -197,3 +197,12 @@ In that case, amplification occurs at the strongest peak of the Raman gain $\til even when the parent pulse is in the NDR. This is an example of stimulated Raman scattering (SRS). + + +## References +1. O. Bang, + *Numerical methods in photonics: lecture notes*, 2019, + unpublished. +2. O. Bang, + *Nonlinear mathematical physics: lecture notes*, 2020, + unpublished. diff --git a/content/know/concept/parsevals-theorem/index.pdc b/content/know/concept/parsevals-theorem/index.pdc index ae34bda..824afa6 100644 --- a/content/know/concept/parsevals-theorem/index.pdc +++ b/content/know/concept/parsevals-theorem/index.pdc @@ -73,3 +73,10 @@ $$\begin{aligned} &= \frac{2 \pi A^2}{|s|} \int_{-\infty}^\infty f^*(x) \: g(x) \dd{x} = \frac{2 \pi A^2}{|s|} \braket{f}{g} \end{aligned}$$ + + + +## References +1. O. Bang, + *Applied mathematics for physicists: lecture notes*, 2019, + unpublished. diff --git a/content/know/concept/partial-fraction-decomposition/index.pdc b/content/know/concept/partial-fraction-decomposition/index.pdc index 1f4207f..7a3847b 100644 --- a/content/know/concept/partial-fraction-decomposition/index.pdc +++ b/content/know/concept/partial-fraction-decomposition/index.pdc @@ -58,3 +58,10 @@ $$\begin{aligned} And then, using the linear independence of $x^0, x^1, x^2, ...$, solving a system of $m$ equations to find all $c_{1,1}, ..., c_{1,m}$. + + + +## References +1. O. Bang, + *Applied mathematics for physicists: lecture notes*, 2019, + unpublished. diff --git a/content/know/concept/probability-current/index.pdc b/content/know/concept/probability-current/index.pdc index c67956a..37cad52 100644 --- a/content/know/concept/probability-current/index.pdc +++ b/content/know/concept/probability-current/index.pdc @@ -96,3 +96,10 @@ $$\begin{aligned} = \mathrm{Re} \Big\{ \psi^* \frac{\hat{p} - q \vec{A}}{m} \psi \Big\} } \end{aligned}$$ + + + +## References +1. L.E. Ballentine, + *Quantum mechanics: a modern development*, 2nd edition, + World Scientific. diff --git a/content/know/concept/rayleigh-plateau-instability/index.pdc b/content/know/concept/rayleigh-plateau-instability/index.pdc index df3d6ab..59407d6 100644 --- a/content/know/concept/rayleigh-plateau-instability/index.pdc +++ b/content/know/concept/rayleigh-plateau-instability/index.pdc @@ -284,6 +284,6 @@ In other words, the liquid column is stable in this case. 1. B. Lautrup, *Physics of continuous matter: exotic and everyday phenomena in the macroscopic world*, 2nd edition, CRC Press. -2. T. Bohr, A. Anderson, +2. T. Bohr, A. Andersen, *The Rayleigh-Plateau instability of a liquid column*, 2020, unpublished. diff --git a/content/know/concept/schwartz-distribution/index.pdc b/content/know/concept/schwartz-distribution/index.pdc index 2d9f9df..bf13f13 100644 --- a/content/know/concept/schwartz-distribution/index.pdc +++ b/content/know/concept/schwartz-distribution/index.pdc @@ -117,3 +117,10 @@ $$\begin{aligned} = \braket*{f}{\tilde{\phi}} } \end{aligned}$$ + + + +## References +1. K.W. Jacobsen, + *Note on generalized functions (distributions)*, 2020, + unpublished. diff --git a/content/know/concept/self-phase-modulation/index.pdc b/content/know/concept/self-phase-modulation/index.pdc index 1ec3fdd..47775b2 100644 --- a/content/know/concept/self-phase-modulation/index.pdc +++ b/content/know/concept/self-phase-modulation/index.pdc @@ -95,3 +95,10 @@ and [dispersion](/know/concept/dispersive-broadening/) leads to many interesting effects, such as [modulational instability](/know/concept/modulational-instability/) and [optical wave breaking](/know/concept/optical-wave-breaking/). + + + +## References +1. O. Bang, + *Numerical methods in photonics: lecture notes*, 2019, + unpublished. diff --git a/content/know/concept/self-steepening/index.pdc b/content/know/concept/self-steepening/index.pdc index 97999b7..256bafb 100644 --- a/content/know/concept/self-steepening/index.pdc +++ b/content/know/concept/self-steepening/index.pdc @@ -143,4 +143,4 @@ $$\begin{aligned} ## References -1. B.R. Suydam, [Self-steepening of optical pulses](https://doi.org/10.1007/0-387-25097-2_6), 2006, Springer Media. +1. B.R. Suydam, [Self-steepening of optical pulses](https://doi.org/10.1007/0-387-25097-2_6), 2006, Springer. diff --git a/content/know/concept/sturm-liouville-theory/index.pdc b/content/know/concept/sturm-liouville-theory/index.pdc index 7ccd625..66a4a82 100644 --- a/content/know/concept/sturm-liouville-theory/index.pdc +++ b/content/know/concept/sturm-liouville-theory/index.pdc @@ -344,3 +344,9 @@ $$\begin{aligned} } \end{aligned}$$ + + +## References +1. O. Bang, + *Applied mathematics for physicists: lecture notes*, 2019, + unpublished. diff --git a/content/know/concept/toffoli-gate/index.pdc b/content/know/concept/toffoli-gate/index.pdc index da5f2a5..f3ab0ba 100644 --- a/content/know/concept/toffoli-gate/index.pdc +++ b/content/know/concept/toffoli-gate/index.pdc @@ -91,3 +91,10 @@ $$\begin{aligned} &= c_{000} \ket{000} + c_{001} \ket{001} + c_{010} \ket{010} + c_{011} \ket{011} \\ &\quad\,\, c_{100} \ket{100} + c_{101} \ket{101} + c_{111} \ket{110} + c_{110} \ket{111} \end{aligned}$$ + + + +## References +1. J.S. Neergaard-Nielsen, + *Quantum information: lectures notes*, + 2021, unpublished. diff --git a/content/know/concept/wetting/index.pdc b/content/know/concept/wetting/index.pdc index 2cb7c08..a3e7c1a 100644 --- a/content/know/concept/wetting/index.pdc +++ b/content/know/concept/wetting/index.pdc @@ -124,3 +124,10 @@ for example, if one is air, we recover the previous case for rough surfaces. Cassie's law can also easily be generalized to three or more materials, and to include Wenzel-style roughness ratios $r_1$, $r_2$, etc. + + +## References +1. T. Bohr, + *Continuum physics: lecture notes*, 2021, + unpublished. + |