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Amith2006
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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?
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 ?
The spin quantum number, denoted as s, is given the value of 1/2 because it represents the intrinsic angular momentum of a particle. This value was determined experimentally and is a fundamental property of particles, similar to their mass or charge.
The spin quantum number tells us about the intrinsic angular momentum of a particle. It is a quantum number that helps to identify and distinguish between different types of particles, such as fermions and bosons.
The spin quantum number is directly related to the spin of a particle. It is a measure of the magnitude of a particle's spin, with values of 1/2 for fermions and whole numbers for bosons. The direction of a particle's spin can be determined by the spin quantum number and the mathematical concept of spin states.
The spin quantum number is important in quantum mechanics because it is one of the fundamental quantum numbers that helps to characterize and describe particles. It is used in equations and calculations to determine properties of particles, and it also plays a role in the Pauli exclusion principle and the concept of spin states.
No, the spin quantum number cannot change. It is a fundamental property of particles that remains constant throughout the particle's existence. However, the direction of a particle's spin can change, but the magnitude of the spin quantum number remains the same.