当年我学到量子场论时，不能理解场算符到底代表什么？
我相信有这种疑惑的不是我一人，所以写在这里请大家讨论。

假设我有一个一米见方的大盒子，里边一个“粒子”
也没有。然后我用比如电子枪打一个电子在盒子里。

我可以说这是在真空中产生了一个动量为q的粒子，但它的位置x
在盒子中何处是不知道的，这个粒子的产生湮灭算符用的是
a_q^\dag和a_q。我又可以说我在真空中x处产生了一个粒子，但它的动量
又是完全不知道的，这个粒子的产生湮灭算符用的\psi^\dag(x)是和\psi(x)。

很显然，这个概念上的模糊来自于量子力学中的测不准关系。
每当我想到在盒子里究竟有什么，在什么状态居然是取决于
我想怎样去看它，我就头晕。这个与我所习惯的图像太不一
样了，我们所要考察的对象到底有没有一个客观存在的，与我们
怎么想无关的东西呢？

相对论量子场论中的场算符\psi(x)不能视为在x处产生一个粒子,见卢里的书.但非相对论量子场论中的可以.

假设我有一个一米见方的大盒子，里边一个“粒子”
也没有。然后我用比如电子枪打一个电子在盒子里。

我可以说这是在真空中产生了一个动量为q的粒子，但它的位置x
在盒子中何处是不知道的，这个粒子的产生湮灭算符用的是
a_q^\dag和a_q。我又可以说我在真空中x处产生了一个粒子，但它的动量
又是完全不知道的，这个粒子的产生湮灭算符用的\psi^\dag(x)是和\psi(x)。
============================================

Please define your thought experiment precisely. What kind of electron-gun you are imagining? Something which only produces electrons with fixed momentum? Or position? Or, are you confused about what an electron-gun will do?

电子枪嘛，就是朝箱子里注入一个电子。
到底是确定的动量还是确定的位置呢？
这个我不太清楚，两者都确定的吧？
就象打在电视屏幕上的电子一样，
位置和动量都可以是确定的。


然后我们等足够长的时间，然后，我们怎么描
述这个电子呢？就回到我的问题了。

电子枪嘛，就是朝箱子里注入一个电子。
到底是确定的动量还是确定的位置呢？
这个我不太清楚，两者都确定的吧？
就象打在电视屏幕上的电子一样，
位置和动量都可以是确定的。

=========================

That is the whole point of your confusion. What the electron will do depends on what is the electron gun, i.e., the preparation of the initial state. We must be very precise in order to answer a physics question.

If you have an electron-gun which can fix momentum precisely, it must be infinitely long (since pure plane-wave is infinitely long). Therefore, you cannot use it to put electron in a box. Therefore, this is not the one you have in mind.

If your electron gun can fix position precisely, it must be infinitely small. You are indeed creating an electron at fixed position. Such an electron does not have a fixed momentum. In fact, it contains all possible momentum with equal portion (only superposition of a complete set of plane-waves gives you delta function). After you created such a state, it will evolve according to Schrodinger equation. Exactly how it will evolve depends on what you mean by box, whether it confines electron or not. After you define the box, the later evolution of such a state is elementary quantum mechanics, Schrodinger equation with initial condition supplied by the initial wave-packet (a delta function in this case).

In real life, of course we cannot have infinitely long or infinitely small electron guns. But, the basic principle still holds. In order to meaningfully talk about "put an electron in a box", the dimension of the electron gun must be smaller than that of the box. It cannot create a plane-wave. At most, it can create a wave-packet of the size of the box. Therefore, it cannot fix momentum up to the precision of the inverse the size of the box. The later evolution of such an state depends on exactly the details of the initial wave-packet, which depends on the details of the electron gun.

就象打在电视屏幕上的电子一样，
位置和动量都可以是确定的。
=============================
The point is that you cannot assign a momentum and position simultaneously base on a measurement. when the electron leaves the electron gun, it is approximately a long wave packet, which could be treated approximately as a momentum eigenstate. It's position is uncertain up to the length of the wave-packet. When it hits the screen, it collapses into a approximate delta -function. After this measurement, one can say the position is approximately fixed. However, we cannot assign the previous momentum to this state anymore since it has been changed.

呵呵，每次问过昌海或你
总是好像弄清了一点。可是过一段时间，
又糊涂了。这次你讲的电子打到屏上时，
有个波包塌缩，确实让我明白了一些。


代我再想一个似是而非例子，放到坛子上来
请教。