複選題17. A harmonic oscillator with charge $q$ is initially in an eigenstate |n. It is subjected to a time-dependent electric field E(t) along the $x$-axis, resulting in the perturbing Hamiltonian H'(t) = -qE(t)x. Based on the properties of the position operator x, which of the following transitions are allowed in first-order perturbation theory? (A) n → n + 1 (B) n → n - 1 (C) n → n + 2 (D) n → n - 2 (E) n → n

複選題

17. A harmonic oscillator with charge $q$ is initially in an eigenstate $|n\rangle$. It is subjected to a time-dependent electric field $\mathcal{E}(t)$ along the $x$-axis, resulting in the perturbing Hamiltonian $\hat{H}'(t) = -q\mathcal{E}(t)\hat{x}$. Based on the properties of the position operator $\hat{x}$, which of the following transitions are allowed in first-order perturbation theory?
(A) $n \to n + 1$
(B) $n \to n - 1$
(C) $n \to n + 2$
(D) $n \to n - 2$
(E) $n \to n$

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B1 · 2026/10/15

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複選題18. In a Compton scattering experiment, the spectrum of scattered X-rays displays two distinct peaks: a modified peak at wavelength $\lambda'$ and an unmodified peak at the incident wavelength $\lambda$. The Compton shift is defined as $\Delta \lambda = \lambda' - \lambda$. Which of the following statements regarding this experiment are correct? (A) The modified peak is due to scattering from loosely bound electrons. (B) The Compton shift $\Delta \lambda$ is independent of the wavelength $\lambda$ of the incident X-ray. (C) The Compton shift $\Delta \lambda$ is always smaller than or equal to zero ($\Delta \lambda \leq 0$). (D) The Compton shift $\Delta \lambda$ depends strongly on the atomic number $Z$ of the target material. (E) The Compton shift $\Delta \lambda$ varies with the scattering angle $\theta$.

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