-. Show explicitly for a harmonic oscillator that ,(x) is orthogonal to , (x), (x), and V,(x) and that ,(x) is orthogonal to ,(x) and y, (x) (see Table 5.3).

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5-16. Show explicitly for a harmonic oscillator that ,(x) is orthogonal to , (x), ½(x), and
V,(x) and that ,(x) is orthogonal to ,(x) and y,(x) (see Table 5.3).
Transcribed Image Text:5-16. Show explicitly for a harmonic oscillator that ,(x) is orthogonal to , (x), ½(x), and V,(x) and that ,(x) is orthogonal to ,(x) and y,(x) (see Table 5.3).
TABLE 5.3
The first few harmonic-oscillator wave functions, Equation 5.35. The parameter
(kµ)2/h.
a =
1/4
1/4
= (x)°
Molt) = ()
V,(x) = ) (2ax – 1)e
%3D
JT
4a/4
1/4
V,(?) = ()
xe-ar/2
a
(2ax' - 3x)e-ax?12
хе
%3|
IT
Transcribed Image Text:TABLE 5.3 The first few harmonic-oscillator wave functions, Equation 5.35. The parameter (kµ)2/h. a = 1/4 1/4 = (x)° Molt) = () V,(x) = ) (2ax – 1)e %3D JT 4a/4 1/4 V,(?) = () xe-ar/2 a (2ax' - 3x)e-ax?12 хе %3| IT
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