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Why is the spin quantum number given a value 1/2? Why not any other value, say +1 for clockwise spin and -1 for anticlockwise spin instead of +1/2 for clockwise spin and -1/2 for anticlockwise spin ?
Are there particles with spin-1 having 3 eigen values -1,0,1? Does 3 eigen values mean that they can have angular momentum due to 3 different spin orientations of the particle?Gokul43201 said:This is not just a convention chosen for convenience. The [itex]\pm \hbar/2 [/itex] comes from the eigenvalues equations for a spin-1/2 particle (like the electron). A spin-1 particle has eigenvalues, -1, 0 and 1, and so on...
The word eigenstate is descriptive of the measured state of some object that possesses quantifiable characteristics such as position, momentum, etc. The state being measured and described must be an "observable" (i.e. something that can be experimentally measured either directly or indirectly like position or momentum), and must have a definite value.Amith2006 said:Are there particles with spin-1 having 3 eigen values -1,0,1? Does 3 eigen values mean that they can have angular momentum due to 3 different spin orientations of the particle?
All spin-1 particles have 3 eigenstates, often represented as something like |+>, |0> and |->, of say, the S_z operator. The probability of observing the particle in any of these 3 states can be any number [itex]0 \leq p \leq 1 [/itex], subject to the condition that the total probability is 1.Amith2006 said:Are there particles with spin-1 having 3 eigen values -1,0,1?
Loosely speaking, yes. But specifically, it means that if you measure say the z-component of the spin, you will observe no more than 3 different values.Does 3 eigen values mean that they can have angular momentum due to 3 different spin orientations of the particle?
Well, the possible values for the spin quantum number come from group theory and are basically determined by symmetry. Symmetry means that the QM equations (like the excpectation value) that describe nature must be invariant under certain transformations like rotations.Amith2006 said:Why is the spin quantum number given a value 1/2? Why not any other value, say +1 for clockwise spin and -1 for anticlockwise spin instead of +1/2 for clockwise spin and -1/2 for anticlockwise spin ?