In[1]:=
No = SqrtB8 a32 “
Π
F
2
2
u = No ã- a x
IntegrateAu2 x2 , 8x, 0, ¥<, Assumptions ® Re@aD > 0E
2 234
Out[1]=
Π14
2 234
Out[2]=
Out[3]=
In[4]:=
a32
a32 ã-a x
2
Π14
1
IntegrateA- x2 u HH1  xL D@D@x u, xD, xD L  2, 8x, 0, ¥<, Assumptions ® Re@aD > 0E
3a
Out[4]=
2
In[5]:=
kin = IntegrateAx2 D@u, xD2 ‘ 2, 8x, 0, ¥<, Assumptions ® Re@aD > 0E
3a
Out[5]=
2
In[7]:=
Out[7]=
In[6]:=
Z=2
2
Upot = IntegrateAx2 u2 H- Z  xL, 8x, 0, ¥<, Assumptions ® Re@aD > 0E
2
Out[6]=
-2
a
Z
Π
In[8]:=
ene = kin + Upot
3a
2
In[9]:=
2
-4
Out[8]=
a
Π
Plot@8kin, Upot<, 8a, 0.8, 1.6<D
2
1
1.0
Out[9]=
-1
-2
-3
-4
1.2
1.4
1.6
2
variat_gaus.nb
In[10]:=
Plot@ene, 8a, 0.8, 1.6<D
-1.64
-1.65
-1.66
Out[10]=
-1.67
-1.68
1.0
In[11]:=
Solve@D@ene, aD Š 0, aD
Out[11]=
::a ®
32
>>
9Π
32
In[12]:=
soluz =
9Π
32
Out[12]=
9Π
1.2
1.4
1.6
variat_gaus.nb
In[13]:=
Π
No = SqrtB8 soluz32 “
F
2
um = No ã- soluz x
32
2
2
3
Out[13]=
3Π
32 x2
32
2
3
-
ã
9Π
Out[14]=
3Π
23
In[15]:=
PlotB:um, Sqrt@4 ΠD
ã-2 x >, 8x, 0, 2<F
Π
5
4
3
2
1
0.5
In[16]:=
1.0
1.5
2.0
kiny = IntegrateA- x2 um HH1  xL D@D@x um, xD, xD L  2, 8x, 0, y<, Assumptions ® Re@aD > 0E
64 y2
-
16 16 ã
9Π
8y
y I- 27 Π + 128 y2 M + 81 Π2 ErfB
3
Out[16]=
243 Π3
Π
F
3
4
variat_gaus.nb
In[17]:=
upoty = IntegrateAx2 um2 H- 2  xL , 8x, 0, y<, Assumptions ® Re@aD > 0E
64 y2
-
32 1 - ã
Out[17]=
9Π
3Π
Plot@8kiny, upoty<, 8y, 0, 3<D
1
0.5
1.0
1.5
2.0
2.5
3.0
-1
-2
-3
23
In[18]:=
ue = Sqrt@4 ΠD
ã-2 x
Π
2 ã-2 x
Out[18]=
4
In[19]:=
kinye = IntegrateA- x2 ue HH1  xL D@D@x ue, xD, xD L  2, 8x, 0, y<, Assumptions ® Re@aD > 0E
Out[19]=
2 + ã-4 y H- 2 + 8 y H- 1 + 2 yLL
variat_gaus.nb
In[20]:=
upotye = IntegrateAx2 ue2 H- 2  xL , 8x, 0, y<, Assumptions ® Re@aD > 0E
Out[20]=
- 4 I1 - ã-4 y H1 + 4 yLM
In[38]:=
Plot@8kiny, kinye, kiny + upoty, kinye + upotye, upoty, upotye<, 8y, 0, 2<D
2
1
0.5
1.0
Out[38]= -1
-2
-3
-4
Plot@8kiny - kinye, upoty - upotye<, 8y, 0, 3<D
0.5
0.5
-0.5
-1.0
1.0
1.5
2.0
2.5
3.0
1.5
5