13. Consider a free electron gas in $d$ spatial dimensions. Let $n$ be the electron number density (defined as the number of electrons per unit length, area, or volume, depending on the dimension). Which of the following correctly describes the dependence of the Fermi energy $E_{F}$ on the density $n$?
(A) $E_{F}\propto n^{2 / d}$
(B) $E_{F}\propto n^{d / 2}$
(C) $E_{F}\propto n$
(D) $E_{F}\propto n^{2}$
(E) $E_{F}\propto n^{1 / d}$

14. Consider a spinless particle in a three-dimensional isotropic simple harmonic oscillator potential. The particle is in an energy eigenstate with eigenenergy: $$ E = \left(99 + \frac{3}{2}\right) \hbar \omega $$ What is the degeneracy of this energy level? (A) 2500 (B) 5151 (C) 10100 (D) 100 (E) 5050

15. The total wavefunction of two electrons is written as a product of a spatial part $\psi(\vec{r}_1, \vec{r}_2)$ and a spin part $\chi_{spin}(s_1, s_2)$. Which of the following combinations correctly describes the symmetry of the spatial and spin parts specifically for the ground state of helium? (A) Spatial part is symmetric; Spin part is antisymmetric. (B) Spatial part is symmetric; Spin part is symmetric. (C) Spatial part is antisymmetric; Spin part is symmetric. (D) Spatial part is antisymmetric; Spin part is antisymmetric. (E) The Pauli principle forbids two electrons from occupying the same 1s spatial orbital, regardless of spin state.

16. Which of the following mathematical expressions correctly represents Planck's formula for the energy density per unit frequency $\rho(\omega)$ of a blackbody at absolute temperature $T$? ($k_B$: Boltzmann constant, $\omega$: angular frequency of light.) (A) $\frac{\hbar \omega^3}{\pi^2 c^3} \frac{1}{e^{\hbar \omega / (k_B T)} - 1}$ (B) $\frac{\hbar \omega^3}{\pi^2 c^3} k_B T$ (C) $\frac{\hbar \omega^3}{\pi^2 c^3} e^{-\hbar \omega / (k_B T)}$ (D) $\frac{\hbar \omega^3}{\pi^2 c^3} \frac{1}{e^{\hbar \omega / (k_B T)} + 1}$ (E) $\frac{\hbar \omega}{e^{\hbar \omega / (k_B T)} - 1}$

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) $n \to n$

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 $\theta$.

複選題19. A Light Emitting Diode (LED) is a p-n junction diode that emits light when activated. Which of the following statements correctly describe the physics and operation of a standard LED? (A) The device must be forward-biased to function properly. (B) The wavelength (color) of the emitted light is primarily determined by the band gap energy $(E_{g})$ of the semiconductor material. (C) The emission process relies on the spontaneous recombination of electron-hole pairs. (D) Indirect band gap semiconductors, such as pure Silicon (Si) or Germanium (Ge), are the most efficient materials for manufacturing visible light LEDs. (E) The intensity of the emitted light decreases as the forward current increases.

複選題20. Which of the following statements regarding the Stern-Gerlach experiment are correct? (A) A non-uniform magnetic field (field gradient) is essential to exert a net force on the particles. (B) The experiment results in a continuous distribution of particles on the detector, as predicted by classical mechanics. (C) The experiment provides direct evidence for the quantization of angular momentum (spin). (D) A beam of neutral silver atoms in their ground state sent through a Stern-Gerlach apparatus will split into two discrete beams. (E) Silver atoms were ideal for the Stern-Gerlach experiment because they possess a single, unpaired valence electron.

1. 向上領導(leading up or upward leadership)是指成員為達成組織或自己的目的，善用其能力與優勢來影響上級領導者與組織的行為。下列何者     不屬於     向上領導的要點？(A) 建立組織層級制度，明確界定上下級關係(B) 瞭解自己的優點、缺點、工作方式、價值觀和組織壓力(C) 努力與上司建立互信互重的工作關係(D) 瞭解上司的優點、缺點、工作方式、價值觀和組織壓力

2. 社會文化與領導的研究中，社會文化學派強調意義之社會建構，屬於跨文化的學校領導研究。根據學者的觀點，在現實層面上，行政實務上的若干文化思想可以為長期堅守的一些教育問題提供可能的解決方案，跨文化研究對於發展更完善的學校領導理論具有重要價值。下列何者     不是     跨文化研究對學校領導的重要貢獻？(A) 專注於單一文化脈絡，強調本土化的特殊性研究(B) 能夠找出具有普遍適用性的共通價值規範(C) 有助於發展更寬廣的研究內涵，顯現以往被忽略的層面(D) 透過跨文化的比較，能夠釐清不同文化間的差異性

3. 依據 Thomas 的雙向度衝突處理模式，當衝突雙方皆展現高度的果決性與合作性時，最可能採取下列哪一種衝突處理方式？(A) 抗爭 (domination)(B) 遮避 (avoidance)(C) 妥協 (compromise)(D) 統合 (collaboration)

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