Quantization 

Quantiza­tion means that certain physi­cal quanti­ties can only take on speci­fic, allowed values, much like steps on a stair­case. Measu­re­ments reveal distinct levels rather than arbitrary inter­me­diate values. This does not imply that all physi­cal quanti­ties are quanti­zed or exhibit discrete values. Depen­ding on the situa­tion, an obser­va­ble may possess a discrete, conti­nuous, or mixed spectrum of possi­ble outco­mes. For example, the energies of bound systems are quanti­zed, whereas position and momen­tum remain conti­nuous varia­bles. Measu­re­ment devices regis­ter this discreten­ess as indivi­dual detec­tion events, often refer­red to as detec­tor clicks, even though the under­ly­ing evolu­tion of the quantum state between measu­re­ments remains smooth and gover­ned by well defined physi­cal laws.

Quantiza­tion challenges the classi­cal notion of unlimi­ted conti­nuity. Reality reveals itself not through an arbitrary range of values, but through a set of permit­ted possi­bi­li­ties. It is precis­ely this struc­ture that makes many quantum pheno­mena, from spectral lines to photons, under­stan­da­ble in the first place.