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複選題20. Which of the following statements are wrong, for a particle totally confined in a 1D asymmetric, piecewise constant potential $V(x)$. (A) The ground state wave function is even in parity. (B) The probability vanishes at infinity. (C) The first excited state is odd in parity. (D) The quantization leads to discrete energy levels. (E) The ground state is non-degenerate.

複選題19. Consider 2 quantum, spin-1/2, non-interacting electrons in a 1D box. Let the box width $L$. Let $n$ = quantum number of the one-electron energy eigenstate with, for example, $n = 0$ for the ground state, $n = 1$ for the 1st excited state, and so on. Denote the two-electron state by $(n_1, n_2)$, where $n_1$ and $n_2$ are the quantum numbers of the one-electron states occupied. Which of the following statements are correct, regarding the two-electron state? (A) The ground state is given by $(n_1 = 0, n_2 = 0)$. (B) The first excited state is given by $(n_1 = 0, n_2 = 1)$. (C) The two spins in the state $(n_1 = 0, n_2 = 0)$ are anti-parallel. (D) The two spins in the state $(n_1 = 0, n_2 = 1)$ can be either parallel or anti-parallel. (E) The two spins in the state $(n_1 = 1, n_2 = 1)$ can be either parallel or anti-parallel.

複選題18. Which of the following statements are correct? (A) According to the Bragg's law, when monochromatic X-rays of wavelength $\lambda = 0.154\,\mathrm{nm}$ are incident on the crystal with lattice spacing $d = 0.5\,\mathrm{nm}$, the first-order diffraction angle $\theta$ is approximately $18^{\circ}$. (B) A spectrometer on Earth with a detection limit of $0.5\,\mathrm{nm}$ can be used to detect the difference between classical and relativistic Doppler's shifts of a star moving toward Earth at a speed of $6\times 10^{6}\,\mathrm{m/s}$ and emitting light at a wavelength of $500\,\mathrm{nm}$. (C) For a free particle in one dimension with the time-dependent Schrödinger wave function $\psi(x,t) = Ae^{i(kx - \omega t)}$, the probability density is independent of time. (D) In the Compton scattering, a photon scattered by a free electron will generally emerge with a longer wavelength if it is deflected through a larger angle. (E) A particle whose wave function is a perfect plane wave has a precisely defined momentum.

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16 行政機關在若干行為領域中,享有所謂「判斷餘地」。有關判斷餘地之說明,下列何者正確? (A)判斷餘地,意指此一領域之決定,絕對不受法院審查 (B)判斷餘地,因必然涉及人民重大基本權,必須有法律之明文依據方予以承認 (C)涉及專業判斷而由具有一定獨立地位委員會所作成之決定,在我國法律中比較容易被承認機關有判斷餘地 (D)判斷餘地,表示機關就特定事務,依法有採取特定措施處理的義務

15. 如下表,所計算之A~I數字,何者為非? (A)B=1,680 (B)C=20 (C)I=3.7 (D)G=2,500。

16. 當存在貨幣幻覺下,勞方貨幣幻覺程度較大時,AS曲線為?(A)正斜率 (B)負斜率 (C)垂直線 (D)水平線。

17. 假設臺灣和美國的資本可以完全自由移動,兩國60天期債券利率分別為:臺灣債券 i = 10\% 、美國債券 \(i^* = 6\%\) ,若今日臺灣的即期美元匯率為32,在60天期的遠期匯率為多少時,你會買美國債券?(A)30 (B)31 (C)33 (D)34。