h*********6
发帖数: 103 | 1 费曼物理讲义第3卷，第2章，2-4 The size of an atom
The spread in momentum is roughly h/a because of the uncertainty relation, …
The momenta must be of the order p~h/a
The total energy = h^2/(2ma^2) – e^2/a
We do not know what a is, but we know the atom is going to arrange itself to
make some kind of compromise so that the energy is as little as possible.
(by solving the derivative of E = 0),
a0=0.528 angstrom
我不懂的是：
（1） 为什么动量的量级就是动量spread的量级？这显然没有必然关系。
（2） 既然说到动量有分布，因为测不准原理；为什么能量又是一个精确数值？
另外，测不准原理只是讲解一 |
t****a
发帖数: 3544 | 2 (1) generally, \Delta p is not necessary comparable to p itself, for
example, classical objects, p >> \Deta p
But, atom is discussed here, where quantum play the key role, and
\Delta p is comparable to p. That is quantum !
(2) Energy is constant in non-relativistic quantum mechanics, which is
the first step to describe the atom.
Energy will also be uncertain for relativistic quantum physics
(3) Uncertainty Principle is the cornerstone of quantum mechanics, of course.
Just as the r
【在 h*********6 的大作中提到】
: 费曼物理讲义第3卷，第2章，2-4 The size of an atom
: The spread in momentum is roughly h/a because of the uncertainty relation, …
: The momenta must be of the order p~h/a
: The total energy = h^2/(2ma^2) – e^2/a
: We do not know what a is, but we know the atom is going to arrange itself to
: make some kind of compromise so that the energy is as little as possible.
: (by solving the derivative of E = 0),
: a0=0.528 angstrom
: 我不懂的是：
: （1） 为什么动量的量级就是动量spread的量级？这显然没有必然关系。
|
h*********6
发帖数: 103 | 3 那测不准原理的表述是不是容易让人误解。
因为如果只是讲观察 （常规意义上的）扰动了粒子，我觉得这个小孩也会理解承认的。
但是我感觉测不准原理似乎有更深层次的意义：
比如观察使得wavefunction collapse。这个是有着重要意义的。
另外，为什么在量子层次上，Delta p is comparable to p. That is quantum !
？？？？？这个是关键。为什么呢？为什么费曼不讲为什么呢？
要多小的粒子，就可以认为Delta p is comparable to p？？
有什么文献可以推荐看看？
course.
【在 t****a 的大作中提到】
: (1) generally, \Delta p is not necessary comparable to p itself, for
: example, classical objects, p >> \Deta p
: But, atom is discussed here, where quantum play the key role, and
: \Delta p is comparable to p. That is quantum !
: (2) Energy is constant in non-relativistic quantum mechanics, which is
: the first step to describe the atom.
: Energy will also be uncertain for relativistic quantum physics
: (3) Uncertainty Principle is the cornerstone of quantum mechanics, of course.
: Just as the r
|
t****a
发帖数: 3544 | 4 measurement problem in quantum physics is indeed still a question nowdays.
But uncertainty princile is equal to say :
particles have wave-like behaviors.
Planck constant provides the criteria of "quantum" usually.
的。
【在 h*********6 的大作中提到】
: 那测不准原理的表述是不是容易让人误解。
: 因为如果只是讲观察 （常规意义上的）扰动了粒子，我觉得这个小孩也会理解承认的。
: 但是我感觉测不准原理似乎有更深层次的意义：
: 比如观察使得wavefunction collapse。这个是有着重要意义的。
: 另外，为什么在量子层次上，Delta p is comparable to p. That is quantum !
: ？？？？？这个是关键。为什么呢？为什么费曼不讲为什么呢？
: 要多小的粒子，就可以认为Delta p is comparable to p？？
: 有什么文献可以推荐看看？
:
: course.
|
C********n
发帖数: 6682 | 5 如果\delta p比 p小数量级的话，你为什么要考虑量子力学呢
feymann不讲可能是因为他觉得这个是大前提
原子级别的东西都可以用这个假定阿
的。
【在 h*********6 的大作中提到】
: 那测不准原理的表述是不是容易让人误解。
: 因为如果只是讲观察 （常规意义上的）扰动了粒子，我觉得这个小孩也会理解承认的。
: 但是我感觉测不准原理似乎有更深层次的意义：
: 比如观察使得wavefunction collapse。这个是有着重要意义的。
: 另外，为什么在量子层次上，Delta p is comparable to p. That is quantum !
: ？？？？？这个是关键。为什么呢？为什么费曼不讲为什么呢？
: 要多小的粒子，就可以认为Delta p is comparable to p？？
: 有什么文献可以推荐看看？
:
: course.
|
h*********6
发帖数: 103 | 6 有可能 p 数量级比delta p小呀。
【在 C********n 的大作中提到】
: 如果\delta p比 p小数量级的话，你为什么要考虑量子力学呢
: feymann不讲可能是因为他觉得这个是大前提
: 原子级别的东西都可以用这个假定阿
:
: 的。
|
h*********6
发帖数: 103 | 7 Your explanation is much better.
But I believe every beginner would mislead if the Uncertainty Principle is
expressed in many quantum mechanics introduction books.
【在 t****a 的大作中提到】
: measurement problem in quantum physics is indeed still a question nowdays.
: But uncertainty princile is equal to say :
: particles have wave-like behaviors.
: Planck constant provides the criteria of "quantum" usually.
:
: 的。
|
C********n
发帖数: 6682 | 8 小的话就是量子效应不显著，不显著你用啥量子力学阿
【在 h*********6 的大作中提到】
: 有可能 p 数量级比delta p小呀。
|
h*********6
发帖数: 103 | 9 现在问的是为什么？
【在 C********n 的大作中提到】
: 小的话就是量子效应不显著，不显著你用啥量子力学阿
|
e********y
发帖数: 935 | 10 所有为什么的答案都是下一个为什么的开始
所以，其实没有为什么，物理学只是给人类提供描述自然的工具
【在 h*********6 的大作中提到】
: 现在问的是为什么？
|
t****a
发帖数: 3544 | 11 Thank you :)
It is a good habit to question textbooks :)
【在 h*********6 的大作中提到】
: Your explanation is much better.
: But I believe every beginner would mislead if the Uncertainty Principle is
: expressed in many quantum mechanics introduction books.
|
e**********n
发帖数: 359 | 12 In the chosen reference frame of this problem, = 0, so p does not give a
relevant scale for momentum or
energy. Please do not confuse the value (matrix element) of an operator and
the operator itself. To write down
a number for momentum in a hand-waving calculation, one naturally considers
moments of the distribution
of p, so is a good candidate, which is clearly related to the 'spread'
of the momentum'.
Whether this kind of argument is acceptable depends on who you're
communicating wi
【在 t****a 的大作中提到】
: Thank you :)
: It is a good habit to question textbooks :)
|
N***m
发帖数: 4460 | 13 I think using the uncertainy principle here is the same
as using the Sommerfeld-Wilson quantization condition. For ground state
which is smooth and no inside node, you can always treat the integral
as something like average quantities, just as in the form of uncertainty
relation. There is no need for vague statements in your arguments.
The average x and p in the simple Hydrogen example turn out to be
in good agreement with the expected values.
a
and
considers
spread'
【在 e**********n 的大作中提到】
: In the chosen reference frame of this problem, = 0, so p does not give a
: relevant scale for momentum or
: energy. Please do not confuse the value (matrix element) of an operator and
: the operator itself. To write down
: a number for momentum in a hand-waving calculation, one naturally considers
: moments of the distribution
: of p, so is a good candidate, which is clearly related to the 'spread'
: of the momentum'.
: Whether this kind of argument is acceptable depends on who you're
: communicating wi
|
