diff options
| -rw-r--r-- | config.toml | 7 | ||||
| -rw-r--r-- | content/blog/2020/email-server.md | 6 | ||||
| -rw-r--r-- | content/know/_index.md | 6 | ||||
| -rw-r--r-- | static/know/concept/blochs-theorem/index.html | 2 |
4 files changed, 11 insertions, 10 deletions
diff --git a/config.toml b/config.toml index 42600c8..b274c73 100644 --- a/config.toml +++ b/config.toml @@ -5,12 +5,13 @@ title = "Prefetch" # Whether to automatically compile all Sass files in the sass directory compile_sass = false +# Whether to build a search index to be used later on by a JavaScript library +build_search_index = false + +[markdown] # Whether to do syntax highlighting # Theme can be customised by setting the `highlight_theme` variable to a theme supported by Zola highlight_code = true -# Whether to build a search index to be used later on by a JavaScript library -build_search_index = false - # Put all your custom variables here [extra] diff --git a/content/blog/2020/email-server.md b/content/blog/2020/email-server.md index 53c13e4..1276552 100644 --- a/content/blog/2020/email-server.md +++ b/content/blog/2020/email-server.md @@ -24,7 +24,7 @@ When you're done, take a look at the [sequel](/blog/2020/email-server-extras/) for ideas to extend your setup. -Last updated 2020-04-29. +Last content update 2020-04-29. Last fix on 2021-02-20. @@ -142,7 +142,7 @@ and a private encryption key at `/etc/ssl/private/example.com.pem`. Obviously, you'll need a server to run the MTA and MDA on. You can host your own at home, but the more reliable option is -to rent one in a data center ([VPS](https://en.wikipedia.org/wiki/Virtual_private_server.)). +to rent one in a data center ([VPS](https://en.wikipedia.org/wiki/Virtual_private_server)). This guide was written with a Linux server in mind, but in theory it should also work on the BSDs ([OpenBSD](https://www.openbsd.org/), [FreeBSD](https://www.freebsd.org/), @@ -687,7 +687,7 @@ Don't worry, the client-server connection is TLS-encrypted, so nobody will be able to steal it. Next, to test sending and receiving messages, -use the aptly-named [Is my email working?](https://ismyemailworking.com/) website. +use the aptly-named [Is my email working?](http://ismyemailworking.com/) website. After that, specifically test that SPF, DKIM an DMARC are working correctly using the [DKIM validator](https://dkimvalidator.com/). If everything is good so far, congratulations! diff --git a/content/know/_index.md b/content/know/_index.md index bf308d9..9e59ffa 100644 --- a/content/know/_index.md +++ b/content/know/_index.md @@ -6,13 +6,13 @@ title = "Knowledge base" Welcome to my knowledge base! -Over the years, I've learned a lot about physics, mathematics, and computing. +Over the years, I've learned a lot of physics, mathematics, and computing. These are vast, difficult subjects, and I've spent many hours of my life trying to make sense of obscure, poorly explained concepts. To help me remember what I learn, I write notes in LaTeX. This knowledge base is based on my notes, and -is freely available to anyone who needs it. +is freely available to anyone who might need it. I hope it helps you in your studies or work. Currently there's isn't much here yet, but I have over 200 pages of LaTeX waiting to be converted. @@ -20,7 +20,7 @@ but I have over 200 pages of LaTeX waiting to be converted. Keep in mind that I'm only human, so there are probably mistakes in my work. I take no responsibility for any injuries incurred as a consequence. -If you're working on something important, +If you're doing something important, you should check things yourself! The contents of this knowledge base are found here: diff --git a/static/know/concept/blochs-theorem/index.html b/static/know/concept/blochs-theorem/index.html index 26e3480..58a934e 100644 --- a/static/know/concept/blochs-theorem/index.html +++ b/static/know/concept/blochs-theorem/index.html @@ -49,7 +49,7 @@ <hr> <h1 id="blochs-theorem">Bloch’s theorem</h1> -<p>In quantum mechanics, <em>Bloch’s theorem</em> states that, given a potential <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo stretchy="false" form="prefix">(</mo><mover><mi>r</mi><mo accent="true">⃗</mo></mover><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">V(\vec{r})</annotation></semantics></math> which is periodic on a lattice, i.e. <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo stretchy="false" form="prefix">(</mo><mover><mi>r</mi><mo accent="true">⃗</mo></mover><mo stretchy="false" form="postfix">)</mo><mo>=</mo><mi>V</mi><mo stretchy="false" form="prefix">(</mo><mover><mi>r</mi><mo accent="true">⃗</mo></mover><mo>+</mo><mover><mi>a</mi><mo accent="true">⃗</mo></mover><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">V(\vec{r}) = V(\vec{r} + \vec{a})</annotation></semantics></math> for a primitive lattice vector <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>a</mi><mo accent="true">⃗</mo></mover><annotation encoding="application/x-tex">\vec{a}</annotation></semantics></math>, then it follows that the solutions <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ψ</mi><mo stretchy="false" form="prefix">(</mo><mover><mi>r</mi><mo accent="true">⃗</mo></mover><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\psi(\vec{r})</annotation></semantics></math> to the time-independent <a href="/know/page/schroedinger-equation">Schrödinger equation</a> take the following form, where the function <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>u</mi><mo stretchy="false" form="prefix">(</mo><mover><mi>r</mi><mo accent="true">⃗</mo></mover><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">u(\vec{r})</annotation></semantics></math> is periodic on the same lattice, i.e. <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>u</mi><mo stretchy="false" form="prefix">(</mo><mover><mi>r</mi><mo accent="true">⃗</mo></mover><mo stretchy="false" form="postfix">)</mo><mo>=</mo><mi>u</mi><mo stretchy="false" form="prefix">(</mo><mover><mi>r</mi><mo accent="true">⃗</mo></mover><mo>+</mo><mover><mi>a</mi><mo accent="true">⃗</mo></mover><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">u(\vec{r}) = u(\vec{r} + \vec{a})</annotation></semantics></math>:</p> +<p>In quantum mechanics, <em>Bloch’s theorem</em> states that, given a potential <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo stretchy="false" form="prefix">(</mo><mover><mi>r</mi><mo accent="true">⃗</mo></mover><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">V(\vec{r})</annotation></semantics></math> which is periodic on a lattice, i.e. <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>V</mi><mo stretchy="false" form="prefix">(</mo><mover><mi>r</mi><mo accent="true">⃗</mo></mover><mo stretchy="false" form="postfix">)</mo><mo>=</mo><mi>V</mi><mo stretchy="false" form="prefix">(</mo><mover><mi>r</mi><mo accent="true">⃗</mo></mover><mo>+</mo><mover><mi>a</mi><mo accent="true">⃗</mo></mover><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">V(\vec{r}) = V(\vec{r} + \vec{a})</annotation></semantics></math> for a primitive lattice vector <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mover><mi>a</mi><mo accent="true">⃗</mo></mover><annotation encoding="application/x-tex">\vec{a}</annotation></semantics></math>, then it follows that the solutions <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ψ</mi><mo stretchy="false" form="prefix">(</mo><mover><mi>r</mi><mo accent="true">⃗</mo></mover><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">\psi(\vec{r})</annotation></semantics></math> to the time-independent Schrödinger equation take the following form, where the function <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>u</mi><mo stretchy="false" form="prefix">(</mo><mover><mi>r</mi><mo accent="true">⃗</mo></mover><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">u(\vec{r})</annotation></semantics></math> is periodic on the same lattice, i.e. <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>u</mi><mo stretchy="false" form="prefix">(</mo><mover><mi>r</mi><mo accent="true">⃗</mo></mover><mo stretchy="false" form="postfix">)</mo><mo>=</mo><mi>u</mi><mo stretchy="false" form="prefix">(</mo><mover><mi>r</mi><mo accent="true">⃗</mo></mover><mo>+</mo><mover><mi>a</mi><mo accent="true">⃗</mo></mover><mo stretchy="false" form="postfix">)</mo></mrow><annotation encoding="application/x-tex">u(\vec{r}) = u(\vec{r} + \vec{a})</annotation></semantics></math>:</p> <p><math display="block" xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mtable><mtr><mtd columnalign="right"><menclose notation="box"><mrow><mi>ψ</mi><mo stretchy="false" form="prefix">(</mo><mover><mi>r</mi><mo accent="true">⃗</mo></mover><mo stretchy="false" form="postfix">)</mo><mo>=</mo><mi>u</mi><mo stretchy="false" form="prefix">(</mo><mover><mi>r</mi><mo accent="true">⃗</mo></mover><mo stretchy="false" form="postfix">)</mo><msup><mi>e</mi><mrow><mi>i</mi><mover><mi>k</mi><mo accent="true">⃗</mo></mover><mo>⋅</mo><mover><mi>r</mi><mo accent="true">⃗</mo></mover></mrow></msup></mrow></menclose></mtd></mtr></mtable><annotation encoding="application/x-tex"> \begin{aligned} \boxed{ |