Question

Consider a particle of mass $m$ subject to a one-dimensional potential of the following form: \[ V=\left\{\begin{array}{ll} \frac{1}{2} k x^{2} & \text { for } x>0 \\ \infty & \text { for } x<0 \end{array}\right. \] (a) What is the ground-state energy? (b) What is the expectation value $\left\langle x^{2}\right\rangle$ for the ground state?

          Consider a particle of mass $m$ subject to a one-dimensional potential of the following form:
\[
V=\left\{\begin{array}{ll}
\frac{1}{2} k x^{2} & \text { for } x>0 \\
\infty & \text { for } x<0
\end{array}\right.
\]
(a) What is the ground-state energy?
(b) What is the expectation value $\left\langle x^{2}\right\rangle$ for the ground state?

Added by Phillip J.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Suman K

06/29/2022

Step 1

The ground state energy of a harmonic oscillator is given by E = (1/2)ħω, where ω = sqrt(k/m) is the angular frequency. Show more…

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Consider a particle of mass $m$ subject to a one-dimensional potential of the following form: \[ V=\left\{\begin{array}{ll} \frac{1}{2} k x^{2} & \text { for } x>0 \\ \infty & \text { for } x<0 \end{array}\right. \] (a) What is the ground-state energy? (b) What is the expectation value $\left\langle x^{2}\right\rangle$ for the ground state?