Pauli Matrix $\sigma_x = |0\rangle\langle 1| + |1\rangle\langle 0|$

Pauli Matrix $\sigma_y = i|0\rangle\langle 1| - i|1\rangle\langle 0|$

Pauli Matrix $\sigma_z = |0\rangle\langle 0| - |1\rangle\langle 1|$

Lowering operator $\sigma_- = |0\rangle\langle 1|$

Raising operator $\sigma_+ = |1\rangle\langle 0|$

rk4(f, y0, tspan, nsteps)

Arguments

• f::Function: function $f(t, y)$ defininf the system of ODEs
• y0::Vector{Float}: inital condition
• tspan::Tuple{Float64}: initial and final time
• nsteps::Int: number of steps.

Returns

An array Array{typeof(y0[1])} with dimensions (ndims(y0), nsteps) with the values of $y$ at each step.