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1.
Given the wavefunction
p(x) = Axe-ax?
that describes a state of a harmonic oscillator provided that the constant a
chosen correctly. Using the potential for a harmonic oscillator
1
1
U(x) =Kx? =-mw?x?
2
2
where w = K
(a) Determine the amplitude A.
(b) Show that the Schrödinger equation is satisfied when a =
and
2h
energy E =hw.

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