Saturday, February 6, 2016

spin http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/mri.html 伊西多·拉比发现在磁场中的原子核会沿磁场方向呈正向或反向有序平行排列,而施加无线电波之后,原子核的自旋方向发生翻转。这是人类关于原子核与磁场以及外加射频场相互作用的最早认识

http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/mri.html

http://sites.uci.edu/energyobserver/2013/02/10/elaboration-of-weak-isospin-and-the-interactions-with-the-weak-bosons-and-the-higgs/

核磁共振成像- 维基百科,自由的百科全书

https://zh.wikipedia.org/zh-hk/核磁共振成像
轉為繁體網頁
核磁共振成像的“核”指的是氢原子核,因为人体的约70%是由水组成的,MRI即依赖 ... 原子核在进动中,吸收与原子核进动频率相同的射频脉冲,即外加交变磁场的 ... 會發出無線電訊號,此訊號藉由電腦的接收並加以分析及轉換處理,可將身體構造及 ...


核磁共振- 维基百科,自由的百科全书

https://zh.wikipedia.org/zh-hk/核磁共振
轉為繁體網頁
3.1 NMR技术; 3.2 MRI技术; 3.3 MRS技术 ... 年代,伊西多·拉比发现在磁场中的原子核会沿磁场方向呈正向或反向有序平行排列,而施加无线电波之后,原子核的自旋方向发生翻转。这是人类关于原子核与磁场以及外加射频场相互作用的最早认识。


核磁共振检查_百度百科

baike.baidu.com/subview/11808034/12179890.htm
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核磁共振检查磁共振成像(Nucler Magnetic Resonance Imaging 简称MRI),是继CT后 ... 其基本原理:是将人体置于特殊的磁场中,用无线电射频脉冲激发人体内氢 ...


核磁_百度百科

baike.baidu.com/view/266810.htm
轉為繁體網頁
其基本原理:是将人体置于特殊的磁场中,用无线电射频脉冲激发人体内氢原子核,引起氢 ... 为了避免与核医学中放射成像混淆,把它称为核磁共振成像术(MRI)。


[PDF]MRI 的射頻線圈1-1

https://www1.cgmh.org.tw/.../e-learning檔案%5C2.1醫學影像%5C2.1.6...
射頻激發. 激發磁場B1 是以拉莫頻率在xy 平面旋轉 z y x. B o. B o. B. 1. M ... 無線電天線的類比. 嚴格說來雖不完全相同但也相當 ... 永久磁鐵MRI 才有螺線管射頻線圈.

Spin in Quantum Mechanics, with Relativity, and the Dirac Equation


This is to elaborate the interactions of the Higgs and the Weak Bosons with the quarks and electrons, specified by the concept of a weak isospin analogous to ordinary spin angular momentum.  This article covers the theory of spin angular momentum.
Quantum mechanics shows that the angular momentum of the smallest pieces of matter is not continuous, but is quantized in units of hbar = h/2π, where hbar is a very small number and h is Planck’s constant.  In regular quantum mechanics for massive atoms at rest, the orbital angular momentum L of an electrons in an atom is quantized in units of hbar, and can be L = n*hbar, where n is an integer, n = 0, 1, 2, etc.  The angular momentum component can only be determined about a one specific axis or direction at a time, and this is usually taken as the z axis or the 3 direction.  The angular momentum component along the z axis, m = Lz, runs through integers from -L to +L.  For L = 0, m = 0.  For L = 1, m = 1, 0, or -1.  For L = 2, m = 2, 1, 0, -1, or -2.  Electromagnetic transitions between different states of the electron conserve Lz when one includes the angular momentum projection of the emitted photon, which is has orbital angular momentum coupled to its spin of 1.
When considering the fundamental particles, relativity must be added to quantum mechanics.  This results in allowing the values of angular momentum of the fundamental particles, called their spin, to include at S = 1/2 hbar, and include 3/2 hbar, etc., along with the integers S = n * hbar.  For a spin 1/2 particles, two values of its spin along the z axis are allowed, Sz = +1/2 hbar, and Sz = -1/2 hbar.  For a massive spin = 1 (S = 1 hbar), just like for orbital angular momentum, Sz = +1, 0, and -1 are allowed.  But for a massless spin 1 particle like the photon, only Sz = +1 and -1 along its direction of motion are allowed.  Spin 1/2 particles are called Fermions and obey Fermi-Dirac statistics and the Pauli Exclusion Principle where two cannot exist in the same state, which builds up the atomic orbitals.  The integer spin particles are called Bosons, and obey Bose-Einstein statistics, where many can exist in the same state.
The spin 1/2 Fermions were actually discovered theoretically when Paul Dirac formulated a relativistic quantum mechanical equation of motion analogous to the Schrodinger equation.
PaulDirac with equation
Another outcome of Dirac’s Equation was the discovery of negative energy states with the same mass but a charge of opposite sign.  This was the discovery of anti-particles, such as the positively charged positron is the anti-particle of the negatively charged electron.
We should add here that in a system with no preferred axis or direction, that is with no outside forces or interactions that have an axis or direction, then the system is invariant or unchanged by rotations.  Rotational invariance leads to the conservation of angular momentum.  This is an example of the Noether theorem formulated by Emmy Noether that associates a conserved quantity with a symmetry.  Emmy Noether (1882-1935) was described as the most important woman in the history of mathematics.
Emmy Noether

An example of a photon interacting with the magnetic moment of a spin 1/2 proton or nucleus in a magnetic field and being absorbed by it to flip its spin to a higher energy state is the basis of nuclear magnetic resonance, now called magnetic resonance imaging:
nmr photon absorption

A moving spin 1/2 particle’s spin can be referred to as along its direction of motion as positive helicity, or right-handed.  If the particle’s spin is opposite its direction of motion, it can be referred to as negative helicity, or left-handed.
Right_left_helicity_svg

Photons, which are massless spin 1 particles, can only have their spin along or opposite their direction of motion, and are then referred to also as right circularly polarized or left circularly polarized, respectively.


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