giann_tee said:Experiments in nuclear magnetic resonance for example, demonstrate that precessing atomic nuclei do it so smoothly. At the same time, atoms have discrete magnetic moments presumably associated with spins. Would anyone care to comment on the difference?
Bob S said:Zeeman effect lines (splitting of characteristic quantized atomic lines) vary smoothly (but not always linearly) with the magnitude of applied magnetic field. The splitting depends on J, L and S.
giann_tee said:I presume, precessing magnetic moments have random phases and then they can collectively precess smoothly. Except "random" means random moment in time to turn discretely. (Ok I'll shut up).
Zapper after 15000 posts its time for you to look back, because you already wrote everything, including the ULTIMATE ANSWER.
giann_tee said:Very interesting. BTW, I encountered this tidbit about most precisely quantized thing...
"The quantization of the Hall conductance has the important property of being incredibly precise. Actual measurements of the Hall conductance have been found to be integer or fractional multiples of e2 / h to nearly one part in a billion. This phenomenon, referred to as "exact quantization", has been shown to be a subtle manifestation of the principle of gauge invariance. "
http://en.wikipedia.org/wiki/Quantum_Hall_effect
ZapperZ said:What does the quantum Hall effect (which involves the supercurrent) have anything to do with your question on NMR, which involves the NUCLEAR magnetic moment?
Zz.
This is a little off-topic, but I just had to ask. Are you saying that QHE is analogous to supercurrent due to the fact that there is no backscattering in a conductor with Landau levels? I mean the situation in which the left and right-moving states are spatially separated.ZapperZ said:What does the quantum Hall effect (which involves the supercurrent) have anything to do with your question on NMR, which involves the NUCLEAR magnetic moment?
saaskis said:This is a little off-topic, but I just had to ask. Are you saying that QHE is analogous to supercurrent due to the fact that there is no backscattering in a conductor with Landau levels? I mean the situation in which the left and right-moving states are spatially separated.
A discrete atom is an atom that is composed of a nucleus, which contains protons and neutrons, and electrons orbiting the nucleus. This means that the atom is made up of distinct and separate particles, rather than being continuous or connected.
The components of an atom, including the nucleus and electrons, are discrete because they are separated by empty space. The nucleus is composed of tiny particles called protons and neutrons, which are held together by strong forces. The electrons are then located in specific energy levels or orbitals around the nucleus, creating distinct boundaries between each component.
While atoms are generally considered to be discrete, there are some exceptions. In certain situations, such as at high temperatures or pressures, atoms can merge and lose their distinct boundaries. Additionally, in some molecules, the electrons are shared between atoms, blurring the lines between individual atoms.
The discreteness of atoms is important in chemistry because it allows us to understand and predict the behavior of atoms and molecules. The distinct boundaries between atoms determine the type of bonds they can form and the resulting chemical properties. Without this discreteness, it would be much more difficult to understand and manipulate the behavior of matter.
The discreteness of atoms was first proposed by ancient Greek philosophers, but it was not until the 19th century that scientists were able to prove it through experiments. In particular, the discovery of the electron by J.J. Thomson in 1897 provided strong evidence for the discreteness of atoms. Since then, advancements in technology, such as scanning tunneling microscopes, have allowed us to directly observe individual atoms and their discrete nature.