Square
well : Unbound states :
R=
T=
Sin 
a (x + 1) ^2
4 x2 + x + Sin 
a (x + 1) ^2
;
4 x2 + x + Sin 
a (x + 1) ^2
;
4 x2 + x
a = 0.1;
Plot[{R, T}, {x, 0, 2},
PlotStyle  {{RGBColor[1, 0, 0], Thickness[0.007`]},
{RGBColor[0, 0, 1], Thickness[0.007`]}}, PlotRange  {0, 1}]
1.0
0.8
0.6
0.4
0.2
0.0
a = 1;
0.5
1.0
1.5
2.0
2
reflection coeffienct.nb
Plot[{R, T}, {x, 0, 2},
PlotStyle  {{RGBColor[1, 0, 0], Thickness[0.007`]},
{RGBColor[0, 0, 1], Thickness[0.007`]}}, PlotRange  {0, 1}]
1.0
0.8
0.6
0.4
0.2
0.0
a = Pi^2;
0.5
1.0
1.5
2.0
Plot[{R, T}, {x, 0, 2},
PlotStyle  {{RGBColor[1, 0, 0], Thickness[0.007`]},
{RGBColor[0, 0, 1], Thickness[0.007`]}}, PlotRange  {0, 1}]
1.0
0.8
0.6
0.4
0.2
0.0
a = 100;
0.5
1.0
1.5
2.0
reflection coeffienct.nb
Plot[{R, T}, {x, 0, 3},
PlotStyle  {{RGBColor[1, 0, 0], Thickness[0.007`]},
{RGBColor[0, 0, 1], Thickness[0.007`]}}, PlotRange  {0, 1}]
1.0
0.8
0.6
0.4
0.2
0.0
a = 250;
0.5
1.0
1.5
2.0
2.5
3.0
Plot[{R, T}, {x, 0, 3},
PlotStyle  {{RGBColor[1, 0, 0], Thickness[0.007`]},
{RGBColor[0, 0, 1], Thickness[0.007`]}}, PlotRange  {0, 1}]
1.0
0.8
0.6
0.4
0.2
0.0
0.5
a = 1000;
1.0
1.5
2.0
2.5
3.0
3
4
reflection coeffienct.nb
Plot[{R, T}, {x, 0, 3},
PlotStyle  {{RGBColor[1, 0, 0], Thickness[0.007`]},
{RGBColor[0, 0, 1], Thickness[0.007`]}}, PlotRange  {0, 1}]
1.0
0.8
0.6
0.4
0.2
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Tunnelling;
R1 =
T1 =
Sinh 
b (1 - y) ^2
4 -y2 + y + Sinh 
b (1 - y) ^2
4 -y2 + y + Sinh 
b (-y + 1) ^2
4 -y2 + y
b = 0.1;
;
;
Plot[{R1, T1}, {y, 0, 1},
PlotStyle  {{RGBColor[1, 0, 0], Thickness[0.007`]},
{RGBColor[0, 0, 1], Thickness[0.007`]}}, PlotRange  {0, 1}]
1.0
0.8
0.6
0.4
0.2
0.0
b = 1;
0.2
0.4
0.6
0.8
1.0
reflection coeffienct.nb
Plot[{R1, T1}, {y, 0, 1},
PlotStyle  {{RGBColor[1, 0, 0], Thickness[0.007`]},
{RGBColor[0, 0, 1], Thickness[0.007`]}}, PlotRange  {0, 1}]
1.0
0.8
0.6
0.4
0.2
0.0
b = Pi^2;
0.2
0.4
0.6
0.8
1.0
Plot[{R1, T1}, {y, 0, 1},
PlotStyle  {{RGBColor[1, 0, 0], Thickness[0.007`]},
{RGBColor[0, 0, 1], Thickness[0.007`]}}, PlotRange  {0, 1}]
1.0
0.8
0.6
0.4
0.2
0.0
b = 64;
0.2
0.4
0.6
0.8
1.0
5
6
reflection coeffienct.nb
Plot[{R1, T1}, {y, 0, 1},
PlotStyle  {{RGBColor[1, 0, 0], Thickness[0.007`]},
{RGBColor[0, 0, 1], Thickness[0.007`]}}, PlotRange  {0, 1}]
1.0
0.8
0.6
0.4
0.2
0.0
0.2
0.4
0.6
0.8
1.0
Scattering
states from a barrier
R2 =
T2 =
Sin 
c (z - 1) ^2
4 z2 - z + Sin 
c (z - 1) ^2
4 z2 - z + Sin
c (z - 1) ^2
4 z2 - z
c = 0.1;
;
;
Plot[{R2, T2}, {z, 1, 4},
PlotStyle  {{RGBColor[1, 0, 0], Thickness[0.007`]},
{RGBColor[0, 0, 1], Thickness[0.007`]}}, PlotRange  {0, 1}]
1.0
0.8
0.6
0.4
0.2
1.0
1.5
2.0
2.5
3.0
3.5
4.0
reflection coeffienct.nb
c = 1;
Plot[{R2, T2}, {z, 1, 4},
PlotStyle  {{RGBColor[1, 0, 0], Thickness[0.007`]},
{RGBColor[0, 0, 1], Thickness[0.007`]}}, PlotRange  {0, 1}]
1.0
0.8
0.6
0.4
0.2
1.0
1.5
c = Pi^2;
2.0
2.5
3.0
3.5
4.0
Plot[{R2, T2}, {z, 1, 4},
PlotStyle  {{RGBColor[1, 0, 0], Thickness[0.007`]},
{RGBColor[0, 0, 1], Thickness[0.007`]}}, PlotRange  {0, 1}]
1.0
0.8
0.6
0.4
0.2
1.0
c = 64;
1.5
2.0
2.5
3.0
3.5
4.0
7
8
reflection coeffienct.nb
Plot[{R2, T2}, {z, 1, 4},
PlotStyle  {{RGBColor[1, 0, 0], Thickness[0.007`]},
{RGBColor[0, 0, 1], Thickness[0.007`]}}, PlotRange  {0, 1}]
1.0
0.8
0.6
0.4
0.2
1.0
1.5
2.0
2.5
3.0
3.5
4.0