Hermitepolynomials19thcenturymathemacs

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Unformatted text preview: ;
a
good
way
to
write
 a
computer
program
doing
harmonic
oscillator
calcula=ons.
 Hermite
polynomials
(19th
century
mathema=cs)
 These
are
“orthogonal”
polynomials,
but
this
doesn’t
mean
what
you
think
it

 might
mean.
 In
general,
orthogonal
polynomials
of
order
k
(=0,1,2
…)
obey
equa=ons
like:
 b Pn (x)Pm (x)w(x)dx = mn a where
n
and
m
are
the
orders
of
the
two
polynomials,
w(x)
is
the
so‐called
 weight
func=on
and
the
thing
on
the
right
hand
side
is
the
ubiquitou...
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This document was uploaded on 03/24/2014.

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