Spin (physics) discrete angular momenta despite having no orbital angular momentum. In some ways, spin is like a vector quantity; it has a definite magnitude, and it has a "direction" (but quantization makes this "direction" different from the direction of an ordinary vector). All elementary particles of a given kind have the same magnitude of spin angular momentum, which is indicated by assigning the particle a spin quantum number. The SI unit of spin is the (N·m·s) or (kg·m·s), just as with classical angular momentum. In practice, spin is given as a dimensionless spin quantum number by dividing the spin angular momentum
Conserved quantity order system of differential equations where bold indicates vector quantities, a scalar-valued function "H"(r) is a conserved quantity of the system if, for all time and initial conditions in some specific domain, Note that by using the multivariate chain rule, so that the definition may be written as which contains information specific to the system and can be helpful in finding conserved quantities, or establishing whether or not a conserved quantity exists. For a system defined by the Hamiltonian "H", a function "f" of the generalized coordinates "q" and generalized momenta "p" has time evolution and hence is conserved if