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## GR0877 Problem 65

PROBLEM STATEMENT: This problem is still being typed.

SOLUTION: (C) Step-by-step elimination. I: true: $E_n = \hbar \omega (n + 1/2)$, this is indeed evenly spaced spectrum; II: false, the potential function is a quadratic function, not linear; III: false, the expectation value of both potential and kinetic energy is half the total energy $\langle V \rangle = \langle T \rangle = \frac{1}{2} \hbar \omega (1+ 1/2)$. Thus, for $n = 0$, $\langle T \rangle \neq 0$. IV: true.

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