作者xavier13540 (柊 四千)
看板NTU-Exam
標題[試題] 102-2 黃暉理 普通物理學甲下 期末考
時間Tue Apr 15 21:49:58 2025
課程名稱︰普通物理學甲下
課程性質︰數學系大一必帶
課程教師︰黃暉理
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰2014/06/17
考試時限（分鐘）：120
試題 :
1. (a) Show the Galilean transformation equations and the Lorentz transforma-
tions. (10 pt.) (b) What is the relation between these two transformations?
(10 pt.) (Note: The four-coordinate (t', x', y', z') detected from S', and
the four-coordinate (t, x, y, z) at S. Frame S' has velocity (v, 0, 0) rela-
tive to frame S and the speed of light is c. Assume the origins of S and S'
coincide at t = t' = 0.)
https://i.imgur.com/jVdUedn.png
\begin{tikzpicture}
\draw (0, 0) -- (.5, 0) node[anchor=west]{$x$};
\draw (0, 0) -- (0, 3) node[anchor=south]{$y$}
node[anchor=north west]{$S$};
\draw (1, 0) -- (3, 0) node[anchor=west]{$x'$};
\draw (1, 0) -- (1, 3) node[anchor=south]{$y'$}
node[anchor=north west]{$S'$};
\draw[thick, -stealth] (1, 2) -- node[midway, below]{$\vec v$} (1.5, 2);
\filldraw (2, 1) circle(2pt);
\draw (2, 1) -- (2.3, 1.6) -- (2.5, 1.6) node[anchor=west]{Particle};
\draw[thick, -stealth] (2, 1) -- (3, 1)
node[anchor=south west]{$\vec u'$ as measured from $S'$}
node[anchor=north west]{$\vec u$ as measured from $S$};
\end{tikzpicture}
2. Figure shows the wave function of the infinite well in 1-dim. (a) What are
the energy, wave function and the probability density of the infinite well
with length L? (15 pt.) (b) Plot the probability density of the well. (5
pt.) (c) Plot the wave function and the probability density if the potential
is finite. (10 pt.) (d) What are the energy and the wave function in the in-
finite square well with length $L_x$ and $L_y$? (10 pt.) (Showing the plot-
ting parts similar to the figure and up to n = 3.)
https://i.imgur.com/EJUt5M9.png
\begin{tikzpicture}
\filldraw[darkgray] (0, 0) -- (0, 5.5) -- (-.5, 5.5) -- (-.5, -.5)
-- (2.5, -.5) -- (2.5, 5.5) -- (2, 5.5) -- (2, 0) -- cycle;
\draw[<->, >=stealth] (0, 6) node[anchor=south]{$\infty$} -- (0, 0)
-- (2, 0) -- (2, 6) node[anchor=south]{$\infty$};
\draw[dotted] (1, 0) -- (1, 5.5);
\draw[<->, >=stealth] (0, .1) -- node[midway, above]{$L$} (2, .1);
\draw[domain=0:2, samples=97, variable=\x] plot(\x, {.5+.4*sin(90*\x)});
\draw[domain=0:2, samples=97, variable=\x] plot(\x, {2.5+.4*sin(180*\x)});
\draw[domain=0:2, samples=97, variable=\x] plot(\x, {4.5+.4*sin(270*\x)});
\draw (0, 1) node[anchor=south west]{$n=1$};
\draw (0, 3) node[anchor=south west]{$n=2$};
\draw (0, 5) node[anchor=south west]{$n=3$};
\draw (1, -.5) node[anchor=north]{$x=0$ at left wall of box.};
\end{tikzpicture}
3. Figure shows a series of Stern-Gerlach analyzers. X and Z shows the direction
of the magnetic field. $N_0 = 1000$ and $N_5 = 250$. (a) What are the numbers
of $N_1$, $N_2$, $N_3$, $N_4$, $N_6$ and $N_7$? (30 pt.) (b) What is the mea-
ning of the Stern-Gerlach experiment? (10 pt.)
https://i.imgur.com/E9mWEMw.png
\begin{tikzpicture}
\draw (-.5, -.5) rectangle (.5, .5);
\draw (0, 0) node{$N_0$};
\draw (.5, 0) -- (1.1, 0);
\draw (1.1, -1) rectangle (3.1, 1);
\draw (2.1, -1) -- (2.1, 1);
\draw (2.1, 0) -- (3.1, 0);
\draw (1.6, 0) node{$Z$};
\draw (2.6, .5) node{$\uparrow$};
\draw (2.6, -.5) node{$\downarrow$};
\draw (3.1, .5) -- (3.7, 1.1) node[anchor=south east]{$N_1$};
\draw (3.7, .1) rectangle (5.7, 2.1);
\draw (4.7, .1) -- (4.7, 2.1);
\draw (4.7, 1.1) -- (5.7, 1.1);
\draw (4.2, 1.1) node{$Z$};
\draw (5.2, 1.6) node{$\uparrow$};
\draw (5.2, .6) node{$\downarrow$};
\draw (5.7, 1.6) -- (6.3, 1.8);
\draw (6.3, 1.3) rectangle (7.3, 2.3);
\draw (6.8, 1.8) node{$N_3$};
\draw (5.7, .6) -- (6.3, .6);
\draw (6.3, .1) rectangle (7.3, 1.1);
\draw (6.8, .6) node{$N_4$};
\draw (3.1, -.5) -- (3.7, -1.1) node[anchor=north east]{$N_2$};
\draw (3.7, -.1) rectangle (5.7, -2.1);
\draw (4.7, -.1) -- (4.7, -2.1);
\draw (4.7, -1.1) -- (5.7, -1.1);
\draw (4.2, -1.1) node{$X$};
\draw (5.2, -.6) node{$\uparrow$};
\draw (5.2, -1.6) node{$\downarrow$};
\draw (5.7, -.6) -- (6.3, -.6);
\draw (6.3, -.1) rectangle (7.3, -1.1);
\draw (6.8, -.6) node{$N_5$};
\draw (5.7, -1.6) -- (6.3, -2.3);
\draw (6.3, -1.3) rectangle (8.3, -3.3);
\draw (7.3, -1.3) -- (7.3, -3.3);
\draw (7.3, -2.3) -- (8.3, -2.3);
\draw (6.8, -2.3) node{$Z$};
\draw (7.8, -1.8) node{$\uparrow$};
\draw (7.8, -2.8) node{$\downarrow$};
\draw (8.3, -1.8) -- (8.9, -1.7);
\draw (8.9, -1.2) rectangle (9.9, -2.2);
\draw (9.4, -1.7) node{$N_6$};
\draw (8.3, -2.8) -- (8.9, -2.9);
\draw (8.9, -2.4) rectangle (9.9, -3.4);
\draw (9.4, -2.9) node{$N_7$};
\end{tikzpicture}
--
第01話 似乎在課堂上聽過的樣子 第02話 那真是太令人絕望了
第03話 已經沒什麼好期望了 第04話 被當、21都是存在的
第05話 怎麼可能會all pass 第06話 這考卷絕對有問題啊
第07話 你能面對真正的分數嗎 第08話 我，真是個笨蛋
第09話 這樣成績，教授絕不會讓我過的 第10話 再也不依靠考古題
第11話 最後留下的補考 第12話 我最愛的學分
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※ 編輯: xavier13540 (36.230.44.40 臺灣), 04/15/2025 21:56:16