From e1ddd40e512f7cfad58eaf7e63ae36a27f9fb971 Mon Sep 17 00:00:00 2001
From: Ian Jauslin <jauslin@ias.edu>
Date: Mon, 1 Oct 2018 22:59:41 +0000
Subject: As presented at Rutgers on 2018-09-27

---
 figs/fowler-nordheim.fig/asymptotic.jl | 46 ++++++++++++++++++++++++++++++++++
 1 file changed, 46 insertions(+)
 create mode 100644 figs/fowler-nordheim.fig/asymptotic.jl

(limited to 'figs/fowler-nordheim.fig/asymptotic.jl')

diff --git a/figs/fowler-nordheim.fig/asymptotic.jl b/figs/fowler-nordheim.fig/asymptotic.jl
new file mode 100644
index 0000000..fd1d492
--- /dev/null
+++ b/figs/fowler-nordheim.fig/asymptotic.jl
@@ -0,0 +1,46 @@
+using QuadGK
+using SpecialFunctions
+using FFTW
+
+# numerical values
+hbar=6.58e-16 # eV.s
+m=9.11e-31 # kg
+Vn=9 # eV
+En=14e9 # V/m
+Kn=4.5 # eV
+
+V=1
+E=En*hbar/(2*Vn^1.5*m^0.5)*sqrt(1.60e-19)
+k0=sqrt(Kn/Vn)
+
+# rescale x to nm
+nm_scale=sqrt(2*m*Vn)/hbar*1e9*sqrt(1.60e-19)
+
+# cutoffs
+p_cutoff=20*k0
+p_npoints=256
+
+# airy approximations
+airy_threshold=30
+airy_order=5
+
+# xbounds
+xmax=10
+xmin=-10
+x_npoints=200
+
+include("FN_base.jl")
+
+# compute asymptotic values
+ps_asym=Array{Complex{Float64}}(undef,x_npoints)
+dps_asym=Array{Complex{Float64}}(undef,x_npoints)
+for i in 1:x_npoints
+  x=xmin+(xmax-xmin)*i/x_npoints
+  ps_asym[i]=psi_pole(x,k0,E,V)
+  dps_asym[i]=dpsi_pole(x,k0,E,V)
+end
+
+# print asymptotic values
+for i in 1:x_npoints
+  print((xmin+(xmax-xmin)*i/x_npoints)*nm_scale,' ',abs(ps_asym[i])^2,' ',J(ps_asym[i],dps_asym[i]),'\n')
+end
-- 
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