P*****s
发帖数: 375 | 1 如果是唯象描述casimir，那有没有谐振子应该关系不大啊，
我认为这个问题跟casimir无关、、
不过我知道好象casimir从经典电动力学加上零点场就可以有唯象解释、、
但是anyway，解一解吧，尤其如果你能解出二维谐振子在圆形无限深
势禁里的能级 (即V=(kr)^2 when rR)
如果能级和拨函数都有，保证你跟我在PRB以上发篇文章:P
曾经问过排骨，他说，基本上，这个很难.. | b***n
发帖数: 6 | 2
Yes, Casimir effect can be described by square well. Suppose
the plane wave solutions are restricted by the boundary
condition, so only some of them survive. The lost zero
energy
will give a force, if it changes with changing the boundary
condition.
Of course, if the boundary is not a square well, other
solutions
other than plane waves should be considered. But I don't
think
the original problem has anything to do with this. It is a
'1D infinite harmonic oscillator', what else can it be????
Num
【在 P*****s 的大作中提到】
: 如果是唯象描述casimir，那有没有谐振子应该关系不大啊，
: 我认为这个问题跟casimir无关、、
: 不过我知道好象casimir从经典电动力学加上零点场就可以有唯象解释、、
: 但是anyway，解一解吧，尤其如果你能解出二维谐振子在圆形无限深
: 势禁里的能级 (即V=(kr)^2 when rR)
: 如果能级和拨函数都有，保证你跟我在PRB以上发篇文章:P
: 曾经问过排骨，他说，基本上，这个很难..
| a*********r
发帖数: 116 | 3 Here is the solution for 2-dimension. The same problem in
one and
three dimensions(for both infinite well and finite well, for
any potential
like r^k) was one of my exercises on quantum mechanics about
ten years ago.
It can be published in Physical Review if it was 75 year
ago.
In atomic unit.
The wavefunction in radial direction:
R(r)=r^|m| exp(-r^2/2)u(r)
m is the angular quantum number
Boundary condition R(a)=0.
u(r) satisfies the equation:
d^2 u/dr^2 + ((2|m|+1)/r-2r)du/dr + (2E-2(|m|+1))u=0 | P*****s
发帖数: 375 | 4 你这堆东西确实是75年前早就有了
see V. Fork, Z. Phys. 47, 446 (1928).
and C. G. Darwin, Proc. Cambridge Philos. Soc. 27, 86 (1930).
我想问的不是这个问题，sorry for confusion,
这几天颇忙，过些天再来post下
thank u for typing these stuff here :)
【在 a*********r 的大作中提到】
: Here is the solution for 2-dimension. The same problem in
: one and
: three dimensions(for both infinite well and finite well, for
: any potential
: like r^k) was one of my exercises on quantum mechanics about
: ten years ago.
: It can be published in Physical Review if it was 75 year
: ago.
: In atomic unit.
: The wavefunction in radial direction:
| a*********r
发帖数: 116 | 5 These two papers have nothing to do with the present
problem. They
are all about parabolic potential. And they are standard
citations in
the textbook on paramagnetic property.
【在 P*****s 的大作中提到】
: 你这堆东西确实是75年前早就有了
: see V. Fork, Z. Phys. 47, 446 (1928).
: and C. G. Darwin, Proc. Cambridge Philos. Soc. 27, 86 (1930).
: 我想问的不是这个问题，sorry for confusion,
: 这几天颇忙，过些天再来post下
: thank u for typing these stuff here :)
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