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.元首. 2013-5-2 02:56 PM

基礎量子力學

用Schrodinger equation所推導出黎既hydrogen atom電子既orbital angular momentum係L=sqrt[l(l+1)]h/2pi
咁即係話, 係1s state, 電子既orbital angular momentum係0 (因為係1s, l=0)
但係用Bohr's model既推導, 係n=1 (n=1中只有1s)係有angular momentum
正常黎講1s亦應該有angular momentum架?
究竟我concept邊到出錯?

Zzlaz 2013-5-6 06:50 PM

FROM WIKI:

The Bohr model gives an incorrect value  for the ground state orbital angular momentum. The angular momentum in the true ground state is known to be zero. Although mental pictures fail somewhat at these levels of scale, an electron in the lowest modern "orbital" with no orbital momentum, may be thought of as not to rotate "around" the nucleus at all, but merely to go tightly around it in an ellipse with zero area (this may be pictured as "back and forth", without striking or interacting with the nucleus). This is only reproduced in a more sophisticated semiclassical treatment like Sommerfeld's. Still, even the most sophisticated semiclassical model fails to explain the fact that the lowest energy state is spherically symmetric--- it doesn't point in any particular direction. Nevertheless, in the modern fully quantum treatment in phase space, Weyl quantization, the proper deformation (full extension) of the semi-classical result adjusts the angular momentum value to the correct effective one. As a consequence, the physical ground state expression is obtained through a shift of the vanishing quantum angular momentum expression, which corresponds to spherical symmetry.
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