Writing Mathematica code in Matlab - matlab

Question

Could anyone please tell me how to do this? I am new to Matlab as well as Mathematica. I have my mathematica coding. But, it gives different results when I run it different time. So, I want to run it in Matlab and verify my result. Please help me anyone.Really appreciate it.
This contains defining functions, parametric plot and etc. I did find thru Matlab. But, I couldn't understand how to write the same program in Matlab.
L1 = 40;
L2 = 20;
A2 = 4.1;
D1 = 1.3;
B1 = 10;
D2 = 19.6;
B2 = 56.6;
N1 = D2 + B2;
N2 = D2 - B2;
A21 = 4.1;
F1 = (D1 \[Pi]^2)/L^2 + (B1 \[Pi]^2)/L^2;
F11 = F1 /. L -> L2;
F2 = (D1 \[Pi]^2)/L^2 - (B1 \[Pi]^2)/L^2;
\[Alpha] = D2^2 - B2^2;
\[Beta] = ((2 \[Pi]^2)/L^2 (D1 D2 - B1 B2) - 2 E1 D2 - A2^2)/\[Alpha];
\[Gamma] = (E1 (E1 - 2 (D1 \[Pi]^2)/L^2) + F1 F2)/\[Alpha];
\[CurlyPhi] = \[Pi]/180*(0);(* input angle in deg*)
\[Kappa]p2 = (-\[Beta] + Sqrt[\[Beta]^2 - 4 \[Gamma]])/2;
\[Kappa]m2 = (-\[Beta] - Sqrt[\[Beta]^2 - 4 \[Gamma]])/2;
\[Kappa]0 = Sqrt[\[Kappa]p2 /. L -> L1];
\[Kappa]01 = Sqrt[-\[Kappa]p2 /. L -> L1];
q = Sqrt[-\[Kappa]m2 /. L -> L1];
q1 = Sqrt[-\[Kappa]p2 /. L -> L2];
q2 = Sqrt[-\[Kappa]m2 /. L -> L2];
(*-----------Electron density \[DoubleStruckCapitalR](\[Rho]) \
:--------------------- *)
R\[Rho] = \[DoubleStruckCapitalN]^2 (p1*Q1*
BesselJ[m, \[Kappa]0*\[Rho]] +
p2*l1*BesselI[m, q*\[Rho]])^2 + \[DoubleStruckCapitalN]^2 (p1*
Q2 BesselJ[m + 1, \[Kappa]0*\[Rho]] +
p2* l2*BesselI[m + 1, q*\[Rho]])^2;
(*\[Rho]<R*)
R\[Rho]1 = \[DoubleStruckCapitalN]^2 (p3*\[CapitalLambda]1*
BesselK[m, q1*\[Rho]] +
p4*\[Beta]1*
BesselK[m,
q2*\[Rho]])^2 + \[DoubleStruckCapitalN]^2 \
(p3*\[CapitalLambda]2*BesselK[m + 1, q1*\[Rho]] +
p4*\[Beta]2*BesselK[m + 1, q2*\[Rho]])^2;(*\[Rho]>R*)
(*---------------Finding p1,p2,p3,p4 -----------------*)
(*
a1 p1+a2 p2+a3 p3==d1;
b1 p1 +b2 p2+b3 p3==d2;
c1 p1+c2 p2+c3 p3==d3;
Subscript[p, 1]=((Subscript[d, 3] Subscript[a, 3]-Subscript[c, 3] \
Subscript[d, 1])(Subscript[b, 2] Subscript[a, 3]-Subscript[b, 3] \
Subscript[a, 2])-(Subscript[d, 2] Subscript[a, 3]-Subscript[b, 3] \
Subscript[d, 1])(Subscript[c, 2] Subscript[a, 3]-Subscript[a, 2] \
Subscript[c, 3]))/((Subscript[c, 1] Subscript[a, 3]-Subscript[c, 3] \
Subscript[a, 1])(Subscript[b, 2] Subscript[a, 3]-Subscript[b, 3] \
Subscript[a, 2])-(Subscript[b, 1] Subscript[a, 3]-Subscript[b, 3] \
Subscript[a, 1])(Subscript[c, 2] Subscript[a, 3]-Subscript[a, 2] \
Subscript[c, 3]));
Subscript[p, 2]=(Subscript[d, 2] Subscript[a, 3]-Subscript[b, 3] \
Subscript[d, 1])/(Subscript[b, 2] Subscript[a, 3]-Subscript[b, 3] \
Subscript[a, 2])-Subscript[p, 1]((Subscript[b, 1] Subscript[a, \
3]-Subscript[b, 3] Subscript[a, 1])/(Subscript[b, 2] Subscript[a, \
3]-Subscript[b, 3] Subscript[a, 2]));
Subscript[p, 3]=Subscript[d, 1]/Subscript[a, 3]-Subscript[a, \
1]/Subscript[a, 3] Subscript[p, 1]-Subscript[a, 2]/Subscript[a, 3] \
Subscript[p, 2
];
Subscript[p, 4]=1;
*)
p1 = -((-b3 c2 d1 + b2 c3 d1 + a3 c2 d2 - a2 c3 d2 - a3 b2 d3 +
a2 b3 d3)/(
a3 b2 c1 - a2 b3 c1 - a3 b1 c2 + a1 b3 c2 + a2 b1 c3 - a1 b2 c3));
p2 = -((b3 c1 d1 - b1 c3 d1 - a3 c1 d2 + a1 c3 d2 + a3 b1 d3 -
a1 b3 d3)/(
a3 b2 c1 - a2 b3 c1 - a3 b1 c2 + a1 b3 c2 + a2 b1 c3 - a1 b2 c3));
p3 = -((-b2 c1 d1 + b1 c2 d1 + a2 c1 d2 - a1 c2 d2 - a2 b1 d3 +
a1 b2 d3)/(
a3 b2 c1 - a2 b3 c1 - a3 b1 c2 + a1 b3 c2 + a2 b1 c3 - a1 b2 c3));
p4 = 1;
a1 = \[Kappa]0 BesselJ[m, \[Kappa]0 R];
a2 = q BesselI[m, q R];
a3 = q1 BesselK[m, q1 R];
b1 = ((F1 /. L -> L1) - E1 + N1 \[Kappa]0^2) BesselJ[
m + 1, \[Kappa]0 R];
b2 = ((F1 /. L -> L1) - E1 - N1 q^2) BesselI[m + 1, q R];
b3 = -(F11 - E1 - N1 q1^2) BesselK[m + 1, q1 R];
c1 = \[Kappa]0^2 BesselJ[m + 1, \[Kappa]0 R];
c2 = -q^2 BesselI[m + 1, q R];
c3 = q1^2 BesselK[m + 1, q1 R];
d1 = -q2 BesselK[m, q2 R];
d2 = (F11 - E1 - N1 q2^2) BesselK[m + 1, q2 R];
d3 = -q2^2 BesselK[m + 1, q2 R];
(*------------Normalization constant---------------*)
\[DoubleStruckCapitalN] =
Sqrt[1/( 2 Pi \
\[DoubleStruckCapitalN]1)];(*1/(\[DoubleStruckCapitalN]^2 2 Pi)=\
\[DoubleStruckCapitalN]1*)
\[DoubleStruckCapitalN]1 = (p1^2*Q1^2*SJJ[m, \[Kappa]0]) + (2*p1*Q1*
p2*l1*SJI[m, \[Kappa]0, q]) + (p2^2*l1^2*SII[m, q]) + (p1^2*Q2^2*
SJJ[m + 1, \[Kappa]0]) + (2*p1*p2*Q2*l2*
SJI[m + 1, \[Kappa]0, q]) + (p2^2*l2^2*
SII[m + 1, q]) + (p3^2*\[CapitalLambda]1^2*SKK[m, q1]) + (2*p3*
p4*\[CapitalLambda]1*\[Beta]1*
SKKab[m, q1, q2]) + (p4^2*\[Beta]1^2*
SKK[m, q2]) + (p3^2*\[CapitalLambda]2^2*SKK[m + 1, q1]) + (2*p3*
p4*\[CapitalLambda]2*\[Beta]2*
SKKab[m + 1, q1, q2]) + (p4^2*\[Beta]2^2*SKK[m + 1, q2]);
Q1 = -A2 \[Kappa]0;
Q2 = (F1 /. L -> L1) - E1 + N1 \[Kappa]0^2;
l1 = -A2 q;
l2 = (F1 /. L -> L1) - E1 - N1 q^2;
\[CapitalLambda]1 = A2 q1;
\[CapitalLambda]2 = F11 - E1 - N1 q1^2;
\[Beta]1 = A2 q2;
\[Beta]2 = F11 - E1 - N1 q2^2;
(*----------Defining the notations----------------*)
SJJ[m_, a_] :=
1/2 R^2 (BesselJ[m, a R]^2 -
BesselJ[-1 + m, a R] BesselJ[m + 1, a R])
SJJab[m_, a_, b_] :=
1/(b^2 - a^2) (a R BesselJ[m, b R ] BesselJ[m - 1, a R] -
b R BesselJ[m - 1, b R] BesselJ[m, a R])
SJI[m_, a_, b_] :=
1/(b^2 + a^2) (-a R BesselI[m, b R ] BesselJ[m - 1, a R] +
b R BesselI[m - 1, b R] BesselJ[m, a R])
SII[m_, a_] :=
1/2 R^2 (BesselI[m, a R]^2 - BesselI[m - 1, a R] BesselI[m + 1, a R])
SIIab[m_, a_, b_] :=
1/(b^2 - a^2) (-a R BesselI[m, b R ] BesselI[m - 1, a R] +
b R BesselI[m - 1, b R] BesselI[m, a R])
SKK[m_, a_] := -(1/2)
R^2 (BesselK[m, a R]^2 - BesselK[m - 1, a R] BesselK[m + 1, a R])
SKKab[m_, a_,
b_] := -(1/(
a^2 - b^2)) (b R BesselK[m, a R ] BesselK[m - 1, b R] -
a R BesselK[m - 1, a R] BesselK[m, b R])
m = 0;
R = 200;
E1 = {0.0888446, 0.153953, 0.24331};
Pm0R200 =
Plot[Piecewise[{{R\[Rho]*10^5, \[Rho] < R}, {R\[Rho]1*10^5, \[Rho] >
R}}], {\[Rho], 0, 250},
AxesLabel -> {Style["\[Rho]", Bold, FontSize -> 18],
Style["|\[CapitalPsi](\[Rho])|\!\(\*SuperscriptBox[\(\\\ \), \
\(2\)]\) (*\!\(\*SuperscriptBox[\(10\), \(-5\)]\))", Bold,
FontSize -> 15]},
BaseStyle -> {FontSize -> 15, FontWeight -> Plain,
FontFamily -> "Times New Roman"}, PlotRange -> Full,
ImageSize -> 700, PlotStyle -> Automatic,
PlotLabel ->
Style["\[DoubleStruckCapitalR](\[Rho]) vs \[Rho] : m=0 & R=200\
\[Angstrom]"]]

Answer 1

Looks like quite a challenge for an inexperienced Matlab user. The Matlab code syntax is different from the Mathematica syntax. You should try to work on something more simple to get to know how Matlab works before trying to write such a difficult script.
Mathworks offers tutorials on their site (I've never done them, but I think it is worth the try) http://www.mathworks.nl/academia/student_center/tutorials/launchpad.html
Also, I found this comparison between the mathematica and matlab syntax, maybe it could help http://amath.colorado.edu/computing/mmm/syntaces.html

Answer 2

Using ToMatlab package you can convert Mathematica expressions to MATLAB equivalents.But it can convert things that have equivalent in MATLAB.
There is a similar question asked in Mathematica.stackexchange.
I don't think conversion of this code to MATLAB is too difficult for a beginner. MATLAB has a very useful ducumentation and you can consult it for your question asked above (about defining functions, Bessel functions, etc in MATLAB)