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3. Show that the wavefunction for the lowest energy state of the simple harmonic oscillator, mwx² Vo(x)= Coe 2h satisfies the time-independent Schrödinger equation for a particle of mass m moving in the potential V(x) = mw²x².

3. Show that the wavefunction for the lowest energy state of the simple harmonic oscillator, mwx² Vo(x)= Coe 2h satisfies the time-independent Schrödinger equation for a particle of mass m moving in the potential V(x) = mw²x².

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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 \[ V(x) = \frac{1}{2} m \omega^2 x^2. \]
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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