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Contoh:<br />
1. Hitunglah gaya pegas rata-rata.<br />
F<br />
Fave = −mω<br />
ψ n ( x)<br />
xψ<br />
n ( x)<br />
dx = −ω<br />
mhω<br />
ψ n ( z)<br />
zψ<br />
n ( z)<br />
dz<br />
2. Hitunglah harga rata-rata energi potensial.<br />
V<br />
=<br />
2<br />
= −mω<br />
x<br />
1<br />
2<br />
2<br />
∞<br />
∫<br />
−∞<br />
mω<br />
2<br />
x<br />
2<br />
∞<br />
∫<br />
2<br />
2<br />
2<br />
Vave =<br />
1<br />
mω ψn<br />
( x)<br />
x ψn<br />
( x)<br />
dx<br />
1<br />
2<br />
= 2 hω<br />
ψn<br />
( z)<br />
z ψn<br />
( z)<br />
dz<br />
−∞<br />
∞<br />
∫<br />
−∞<br />
∞<br />
∫<br />
−∞<br />
3. Hitunglah harga rata-rata energi kinetik<br />
K<br />
K<br />
2 2<br />
h d<br />
= −<br />
2<br />
2m<br />
dx<br />
ave<br />
2<br />
h<br />
= −<br />
2m<br />
∞<br />
∫<br />
−∞<br />
ψ<br />
n<br />
⎡ d<br />
( x)<br />
⎢<br />
⎣dx<br />
2<br />
2<br />
ψ<br />
n<br />
⎤<br />
( x)<br />
⎥dx<br />
=<br />
⎦<br />
−<br />
1<br />
2<br />
hω<br />
∞<br />
∫<br />
−∞<br />
ψ<br />
n<br />
⎡ d<br />
( z)<br />
⎢<br />
⎣dz<br />
2<br />
2<br />
ψ<br />
n<br />
⎤<br />
( z)<br />
⎥dz<br />
⎦<br />
50
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