add hw9 and hw8

1 files changed, 19 insertions, 19 deletions

diff --git a/hw8/TimeDependentSchrodingerEquation.jl b/hw8/TimeDependentSchrodingerEquation.jl
index dacbced..1d4f315 100644
--- a/hw8/TimeDependentSchrodingerEquation.jl
+++ b/hw8/TimeDependentSchrodingerEquation.jl
@@ -7,26 +7,26 @@ using DifferentialEquations
 # useful functions:
 
 function H(psi, dx) # action of Hamiltonian on wavefunction
-    Hpsi = zeros(ComplexF64, size(psi))
-    # -(1/2) * laplacian(psi) (m = hbar = 1)
-    Hpsi[2:end-1] = 0.5 * (2.0*psi[2:end-1] - psi[3:end] - psi[1:end-2])/(dx*dx)
-
-    # periodic boundary conditions
-    #Hpsi[1] = 0.5 * (2.0*psi[1] - psi[2] - psi[end])/(dx*dx)
-    #Hpsi[end] = 0.5 * (2.0*psi[end] - psi[end-1] - psi[1])/(dx*dx)
-    return Hpsi
+	Hpsi = zeros(ComplexF64, size(psi))
+	# -(1/2) * laplacian(psi) (m = hbar = 1)
+	Hpsi[2:end-1] = 0.5 * (2.0 * psi[2:end-1] - psi[3:end] - psi[1:end-2]) / (dx * dx)
+
+	# periodic boundary conditions
+	#Hpsi[1] = 0.5 * (2.0*psi[1] - psi[2] - psi[end])/(dx*dx)
+	#Hpsi[end] = 0.5 * (2.0*psi[end] - psi[end-1] - psi[1])/(dx*dx)
+	return Hpsi
 end
 
 derivative(psi, dx) = -1.0im * H(psi, dx)
 
 function initialWavefunction(x::Vector{Float64}, x0 = 10.0, Delta = 1.0, k = 4.0)
-    Delta2 = Delta^2
-    return exp.(- (x .- x0).^2 / Delta2 ) .* exp.(1.0im * k * x)
+	Delta2 = Delta^2
+	return exp.(-(x .- x0) .^ 2 / Delta2) .* exp.(1.0im * k * x)
 end
 
 function normalization(psi, dx) # normalization of wavefunction
-    n2 = dot(psi, psi) * dx
-    return sqrt(n2)
+	n2 = dot(psi, psi) * dx
+	return sqrt(n2)
 end
 
 prob(psi) = real(psi .* conj(psi))
@@ -56,17 +56,17 @@ dt = 0.0001
 tspan = (0.0, tf)
 
 function timeEvolve(psi0, tf, dt) # second order Runge-Kutta algorithm
-    psi = psi0
-    for t in range(0, stop=tf, step=dt)
-        psiMid = psi + 0.5 * dt * derivative(psi, dx)
-        psi = psi + dt * derivative(psiMid, dx)
-    end
-    return psi
+	psi = psi0
+	for t in range(0, stop = tf, step = dt)
+		psiMid = psi + 0.5 * dt * derivative(psi, dx)
+		psi = psi + dt * derivative(psiMid, dx)
+	end
+	return psi
 end
 
 tendency(psi, dx, t) = derivative(psi, dx) # use ODE solver
 problem = ODEProblem(tendency, psi0, tspan, dx) # specify ODE
-sol = solve(problem, Tsit5(), reltol=1e-12, abstol=1e-12) # solve using Tsit5 algorithm to specified accuracy
+sol = solve(problem, Tsit5(), reltol = 1e-12, abstol = 1e-12) # solve using Tsit5 algorithm to specified accuracy
 
 # compare initial and final wavefunction probabilities
 #psi = timeEvolve(psi0, tf, dt)