Consider the wave function for the ground state harmonic oscillator: \[ \psi(x) = \left( \frac{m \omega}{\pi \hbar} \right)^{1/4} e^{-m \omega x^2 / (2 \hbar)} \] A. What is the quantum number for this ground state? \( \nu = \) \( \boxed{0} \) B. Enter the integrand you'd need to evaluate \(\langle x \rangle\) for the ground state harmonic oscillator wave function: \[ \langle x \rangle = \int_{-\infty}^{\infty} \left( \left( \frac{m \omega}{\pi \hbar} \right)^{1/2} e^{-m \omega x^2 / \hbar} \right) x \, dx \] C. Evaluate the integral in part B. What do you obtain for the average displacement? \( \boxed{0} \)
Consider the wave function for the ground state harmonic oscillator: \[ \psi(x) = \left( \frac{m \omega}{\pi \hbar} \right)^{1/4} e^{-m \omega x^2 / (2 \hbar)} \] A. What is the quantum number for this ground state? \( \nu = \) \( \boxed{0} \) B. Enter the integrand you'd need to evaluate \(\langle x \rangle\) for the ground state harmonic oscillator wave function: \[ \langle x \rangle = \int_{-\infty}^{\infty} \left( \left( \frac{m \omega}{\pi \hbar} \right)^{1/2} e^{-m \omega x^2 / \hbar} \right) x \, dx \] C. Evaluate the integral in part B. What do you obtain for the average displacement? \( \boxed{0} \)
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![Consider the wave function for the ground state harmonic oscillator:
\[
\psi(x) = \left( \frac{m \omega}{\pi \hbar} \right)^{1/4} e^{-m \omega x^2 / (2 \hbar)}
\]
A. What is the quantum number for this ground state? \( \nu = \) \( \boxed{0} \)
B. Enter the integrand you'd need to evaluate \(\langle x \rangle\) for the ground state harmonic oscillator wave function:
\[
\langle x \rangle = \int_{-\infty}^{\infty} \left( \left( \frac{m \omega}{\pi \hbar} \right)^{1/2} e^{-m \omega x^2 / \hbar} \right) x \, dx
\]
C. Evaluate the integral in part B. What do you obtain for the average displacement? \( \boxed{0} \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa0bb33da-4292-4a51-8799-113a66f1981e%2F81b8e85c-c1bc-4402-87ed-47036dd95790%2Fqiv2qru_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the wave function for the ground state harmonic oscillator:
\[
\psi(x) = \left( \frac{m \omega}{\pi \hbar} \right)^{1/4} e^{-m \omega x^2 / (2 \hbar)}
\]
A. What is the quantum number for this ground state? \( \nu = \) \( \boxed{0} \)
B. Enter the integrand you'd need to evaluate \(\langle x \rangle\) for the ground state harmonic oscillator wave function:
\[
\langle x \rangle = \int_{-\infty}^{\infty} \left( \left( \frac{m \omega}{\pi \hbar} \right)^{1/2} e^{-m \omega x^2 / \hbar} \right) x \, dx
\]
C. Evaluate the integral in part B. What do you obtain for the average displacement? \( \boxed{0} \)
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