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The function Psi(x) displayed in Eq. 37-...

The function `Psi(x)` displayed in Eq. 37-19 can describe a free particle, for which the potential energy is U(x) = 0 in Schrodinger's equation (Eq. 37-11). Assume now that `U(x)=U_(0)= a` constant in that equation. Show that Eq. 37-19 is a solution of Schrodinger's equation, with
`k=(2pi)/(h)sqrt(2m(E-U_(0))`
giving the angular wave number k of the particle.

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