朱莉娅3d晶格上随时间变化的薛定inger方程 [英] Time-dependent Schrodinger equation on 3d lattice in Julia

问题描述

我想使用 DifferentialEquations.jl来解决3d晶格上矩阵形式的时间相关Schrodinger方程，

即（∂/∂t）ψ= -i H ψ，其中ψ是一个向量，H是一个（与时间无关的）矩阵。 br />
我试图编写这样的代码。

I want to solve the matrix-form time-dependent Schrodinger equation on 3d lattice with DifferentialEquations.jl,
i.e., (∂/∂t)ψ = -iHψ ,where ψ is a vector and H is a (time-independent) matrix.
I tried to write the code like this.

#Define the underlying equation
function time_evolution(ψdot,ψ,p,t)
  ψdot.=-im.*H(Lx,Ly,Lz)*ψ
end

Lx = Ly = Lz = 10
ψ0 = [] #  Initial conditions
σ = sqrt(5/2)

for iz = 1:Lz
    for ix = 1:Lx
        for iy = 1:Ly                  
           gauss = (1/(sqrt(2*π)*σ)^3)*exp(-((ix)^2 + (iy)^2 + (iz)^2)/(2*(σ)^2))
           push!(ψ0,gauss)                           
        end
    end
end

tspan = (0.,1.0) #  Simulation time span


#Pass to Solvers
prob = ODEProblem(time_evolution,ψ0,tspan)
sol = solve(prob)

这里，H（Lx，Ly，Lz）是一个N×N矩阵，由系统大小Lx，Ly，Lz和N = Lx×Ly×Lz来参数化。 />
但是此代码有错误。

Here,H(Lx,Ly,Lz) is a N×N matrix parameterized by systemsize Lx,Ly,Lz and N = Lx×Ly×Lz.
But this code has an error.

StackOverflowError:
Stacktrace:
 [1] recursive_unitless_bottom_eltype(::Type{Any}) at 
/Users/username/.julia/packages/RecursiveArrayTools/OAIEc/src/utils.jl:86 (repeats 
80000 times)

代码中的错误在哪里？

推荐答案

ψ0 = [] #  Initial conditions

您可能不希望方程式为非具体类型，因此您可能想这样做

You probably don't want your equation to be non-concretely typed, so you likely want to do

ψ0 = Float64[] #  Initial conditions

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