8 classicalturning points 06 04 02 0 10 5 0 5 10 1

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Unformatted text preview: interval
extending
over
the
en=re
x
axis
 ( ⇥ , ⇥) Convince
yourself
from
this
that
the
harmonic
oscillator
wavefunc=ons
are
orthogonal.
 In
the
following,
we
will
use
“reduced”
(dimensionless)
coordinates
defined
by
 q= x which
are
quite
convenient
and
oWen
used
by
people
like
me.


With
these

 coordinates,
the
following
condi=ons
hold
 n ( x) q2 = Nn Hn (q ) exp( Nn = qtp ⇤ = 1 1 2n n! 2(n + 2 ⇥ 1/4 1 2 ) ) ⇥ 1 /2 The
last
of
these
equa=ons
may
not
be
obvious,
but
its
deriva=on
is
simple:
 qtp 2E = k 2m⇥ E = = = ⇥1 / 2 ⇤ k ⇥ 1/2 2m⇥ [ ⇥...
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This document was uploaded on 03/24/2014.

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