Bike-friendly cities, off-road paths, and scenic country roads where cyclists can spin along in comfort aren't just good for the people who live in those places.
Even though cranks had an overrun mechanism, when the engine started, the crank could begin to spin along with the crankshaft and potentially strike the person cranking the engine.
The spin-lowering operator annihilates the state with minimum projection of spin along the -axis, while the spin-raising operator annihilates the ground state with maximum spin projection along the -axis.
Each magnon reduces the total spin along the direction of magnetization by one unit of and the magnetization itself by, where is the gyromagnetic ratio.