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![**Problem 3:**
Show that the wavefunction for the lowest energy state of the simple harmonic oscillator,
\[
\Psi_0(x) = C_0 e^{-\frac{m \omega x^2}{2 \hbar}}
\]
satisfies the time-independent Schrödinger equation for a particle of mass \( m \) moving in the potential
\[
V(x) = \frac{1}{2} m \omega^2 x^2.
\]](https://content.bartleby.com/qna-images/question/e6208a55-bec6-433a-a894-0742aca7c9d7/a71a84b3-6e0d-4bc5-b4a9-52f637f0bbbd/14tb1d_processed.jpeg)
Transcribed Image Text:**Problem 3:**
Show that the wavefunction for the lowest energy state of the simple harmonic oscillator,
\[
\Psi_0(x) = C_0 e^{-\frac{m \omega x^2}{2 \hbar}}
\]
satisfies the time-independent Schrödinger equation for a particle of mass \( m \) moving in the potential
\[
V(x) = \frac{1}{2} m \omega^2 x^2.
\]
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