<s>
In	O
numerical	B-General_Concept
analysis	I-General_Concept
,	O
the	O
shooting	B-Algorithm
method	I-Algorithm
is	O
a	O
method	O
for	O
solving	O
a	O
boundary	O
value	O
problem	O
by	O
reducing	O
it	O
to	O
an	O
initial	O
value	O
problem	O
.	O
</s>
<s>
The	O
shooting	B-Algorithm
method	I-Algorithm
is	O
the	O
process	O
of	O
solving	O
the	O
initial	O
value	O
problem	O
for	O
many	O
different	O
values	O
of	O
until	O
one	O
finds	O
the	O
solution	O
that	O
satisfies	O
the	O
desired	O
boundary	O
conditions	O
.	O
</s>
<s>
Typically	O
,	O
one	O
does	O
so	O
numerically	B-Algorithm
.	O
</s>
<s>
The	O
term	O
"	O
shooting	B-Algorithm
method	I-Algorithm
"	O
has	O
its	O
origin	O
in	O
artillery	O
.	O
</s>
<s>
The	O
trajectory	O
that	O
"	O
hits	O
"	O
the	O
desired	O
boundary	O
value	O
is	O
the	O
solution	O
to	O
the	O
boundary	O
value	O
problem	O
—	O
hence	O
the	O
name	O
"	O
shooting	B-Algorithm
method	I-Algorithm
"	O
.	O
</s>
<s>
The	O
shooting	B-Algorithm
method	I-Algorithm
can	O
also	O
be	O
used	O
to	O
solve	O
eigenvalue	O
problems	O
.	O
</s>
<s>
Consider	O
the	O
time-independent	O
Schrödinger	O
equation	O
for	O
the	O
quantum	O
harmonic	O
oscillatorIn	O
quantum	O
mechanics	O
,	O
one	O
seeks	O
normalizable	O
wavefunctions	O
and	O
their	O
corresponding	O
energies	O
subject	O
to	O
the	O
boundary	O
conditions	O
The	O
problem	O
can	O
be	O
solved	O
analytically	O
to	O
find	O
the	O
energies	O
for	O
,	O
but	O
also	O
serves	O
as	O
an	O
excellent	O
illustration	B-Algorithm
of	I-Algorithm
the	I-Algorithm
shooting	I-Algorithm
method	I-Algorithm
.	O
</s>
<s>
To	O
find	O
the	O
-th	O
excited	O
state	O
and	O
its	O
energy	O
,	O
the	O
shooting	B-Algorithm
method	I-Algorithm
is	O
then	O
to	O
:	O
</s>
