Re: Schroedinger EQ

• To: mathgroup at smc.vnet.net
• Subject: [mg122037] Re: Schroedinger EQ
• From: raj kumar <rajesh7796gm at gmail.com>
• Date: Mon, 10 Oct 2011 04:27:18 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j6q61b\$p1g\$1@smc.vnet.net>

```sorry,  A =82

On Oct 9, 2:50 am, raj kumar <rajesh779... at gmail.com> wrote:
> dear esteemed experts,
>
> i wonder if somebody can help me
>
> i have been trying to find a a certain value of a parameter V that
> will "match" the logarithmic derivative (of solutions to the time
> independent Schroedinger eq ) at both sides of a particular point
> called the matching point. But cannot seem to find the correct V value
> that will make
> bc1[V_] = bc2[V_].. ...mathematica keeps giving an error message .See
> below for the code.
>
> any help will be most appreciated
>
> a=0.63;
> A8;
> j=9/2;
> L=4;
> mu=(931.5 (208 1.))/(208+1.);
> Z=82;
>  Subscript[a, so]=0.5;
> R=1.25 A^(1/3);
> Subscript[V, so]=7;
> Subscript[R, c]=1.25 A^(1/3);
> Subscript[R, so]=1.1 A^(1/3);
>  V1[x_,V_]:=-(V/(E^((x-R)/a)+1)); V2[x_]:=-((2 ((j+1) j-L (L+1)-3/4=
)
> Subscript[V, so] E^((x-Subscript[R, so])/Subscript[a, so]))/
> (Subscript[a, so] (E^((x-Subscript[R, so])/Subscript[a, so])+1)^2));
> pott[x_,V_]=V1[x,V]+V2[x];
>
> emin=-55;
> emax=  -5;
> xmax=10;
> xmin=0.1;
> xmatch=4.5;
> e=3.94;
>
> eq[V_, x_, x0_] = {-(
> \!\(\*SuperscriptBox["y", "\[Prime]\[Prime]",
> MultilineFunction->None]\)[x]/(
>       2 mu)) + (pott[x, V] + L (L + 1)/(2 mu (x^2))) y[x] == -e=
y[x],
>    y[x0] == 0,
> \!\(\*SuperscriptBox["y", "\[Prime]",
> MultilineFunction->None]\)[x0] == 1/10^6};
> y1[V_, x_] := y[x] /. NDSolve[eq[V, x, xmin], y, {x, xmin, xmatch}];
> bc1[V_] := \!\(
> \*SubscriptBox[\(\[PartialD]\), \(x\)]\(y1[x]\)\)/y1[x] /. x ->
> xmatch;
> y2[V_, x_] := y[x] /. NDSolve[eq[V, x, xmax], y, {x, xmax, xmatch}];
> bc2[V_] := \!\(
> \*SubscriptBox[\(\[PartialD]\), \(x\)]\(y2[x]\)\)/y2[x] /. x ->
> xmatch;
> bc[V_?NumericQ] := bc1[V] - bc2[V];
> Vvalue = V /.
>    If[emax == emin, V,
>     FindRoot[bc[V], {V, emin, emax}, AccuracyGoal -> 10,
>      WorkingPrecision -> 20]];
> Print["the value of V is =" , Vvalue]

```

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