braket.jl

#+BEGIN_SRC julia
const ketpat = r"\|.*?\>"
ketrep(str) = "Ket("*(match(r"(?<=\|).*?(?=>)", str).match)*")"

const brapat = r"\<.*?\|"
brarep(str) = "Bra("*(match(r"(?<=<).*?(?=\|)", str).match)*")"

function rep_braket(str)
    replace(replace(str, brapat => brarep), ketpat => ketrep)
end

parse_braket(str) = Meta.parse(rep_braket(str))

macro d_cmd(str)
    esc(parse_braket(str))
end

Ket(args...) = [args...]
Ket(a::Vector) = a

Bra(args...) = [args...]'
Bra(a::Vector) = a'

Ket(a::Vector) = a
Bra(a::Vector) = a'

↑ = [1, 0]
↓ = [0, 1];

σz = d`|↑>*<↑| - |↓>*<↓|`
#+END_SRC

#+RESULTS:
: 2×2 Array{Int64,2}:
:  1   0
:  0  -1


#+BEGIN_SRC julia
→ = d`(|↑⟩ + |↓⟩)/√2`
← = d`(|↑⟩ - |↓⟩)/√2`

d```
 [⟨→|*σz*|→⟩ ⟨→|*σz*|←⟩
  ⟨←|*σz*|→⟩ ⟨←|*σz*|←⟩]
```
#+END_SRC

#+RESULTS:
: 2×2 Array{Float64,2}:
:  0.0  1.0
:  1.0  0.0