Fraktur list

upp. low. upp. low. upp. low.
\mathfrak{A} \mathfrak{a} [aː] \mathfrak{J} \mathfrak{j} [yɔt] \mathfrak{S} \mathfrak{s} [ɛs]
\mathfrak{B} \mathfrak{b} [beː] \mathfrak{K} \mathfrak{k} [kaː] \mathfrak{T} \mathfrak{t} [teː]
\mathfrak{C} \mathfrak{C} [tseː] \mathfrak{L} \mathfrak{L} [ɛl] \mathfrak{U} \mathfrak{u} [uː]
\mathfrak{D} \mathfrak{d} [deː] \mathfrak{M} \mathfrak{m} [ɛm] \mathfrak{V} \mathfrak{v} [faʊ]
\mathfrak{E} \mathfrak{e} [eː] \mathfrak{N} \mathfrak{n} [ɛn] \mathfrak{W} \mathfrak{w} [veː]
\mathfrak{F} \mathfrak{f} [ɛf] \mathfrak{O} \mathfrak{o} [oː] \mathfrak{X} \mathfrak{x} [iks]
\mathfrak{G} \mathfrak{g} [geː] \mathfrak{P} \mathfrak{p} [peː] \mathfrak{Y} \mathfrak{y} ['ypsilcn]
\mathfrak{H} \mathfrak{h} [haː] \mathfrak{Q} \mathfrak{q} [kuː] \mathfrak{Z} \mathfrak{z} [ɛstsɛt]
\mathfrak{I} \mathfrak{i} [iː] \mathfrak{R} \mathfrak{r} [əʁ]

One of numerical solution of de Broglie's wave equation

I am not a specialist of Physics. This is my trial, if there are inappropriate moment, I would like you to let me know. Long movie with high frame per second rate. I wanted to see a stationary wave, but I could not.

I was very surprised when I see the equation first time because by only introducing complex number to a wave equation, we can obtain directed wavelet. In my traditional knowledge, linear equation never produce such asymmetric result. For example, in fluid dynamics, we need convection term, which is strongly non-linear term, to produce directed flow.