作者xavier13540 (柊 四千)
看板NTU-Exam
标题[试题] 102-2 黄晖理 普通物理学甲下 期末考
时间Tue Apr 15 21:49:58 2025
课程名称︰普通物理学甲下
课程性质︰数学系大一必带
课程教师︰黄晖理
开课学院：理学院
开课系所︰数学系
考试日期（年月日）︰2014/06/17
考试时限（分钟）：120
试题 :
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话 似乎在课堂上听过的样子 第02话 那真是太令人绝望了
第03话 已经没什麽好期望了 第04话 被当、21都是存在的
第05话 怎麽可能会all pass 第06话 这考卷绝对有问题啊
第07话 你能面对真正的分数吗 第08话 我，真是个笨蛋
第09话 这样成绩，教授绝不会让我过的 第10话 再也不依靠考古题
第11话 最後留下的补考 第12话 我最爱的学分
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※ 编辑: xavier13540 (36.230.44.40 台湾), 04/15/2025 21:56:16