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Quantization (in theoretical physics) covers any mathematical method of developing a theory which incorporates quantum theoretical ideas from a classical concept. The most dramatic might be Quantum Electrodynamics (QED) which is developing a theory for the electromagnetic field from quantum ideas. The resulting theory can get us back to Maxwell ...
(a) definition of quantization; (b) why do we need quantum mechanics; (c) what is the difference between classical and quantum mechanics; (d) combination of (a),(b),(c) or others. Quantum mechanics differs the classical least action principle, since the operators do not commute.
$\begingroup$ An example of a quantum phenomenon that fails to emerge from naive quantization is the Pauli Exclusion Principle. But I agree with you that quantization is a valuable technique that often yields workable models. However, this is physics, not math. Rigor is neither necessary nor sufficient as a path to a good model.
Quantisation does not imply discreteness. In fact the opposite is true, they are very different concepts. Part of the answer is in the definition of "discrete". Practical examples: Quantisation: Consider the photon as discrete packets of energy ℏω as mentioned in the question. Using this equation and the fixed speed of light, a "red" photon ...
Aug 25, 2016 at 13:19. @garyp: In definition 1, the π π -polarization is a sum of σ+ σ + and σ− σ −. If in definition 2 saying "with jz = mℏ j z = m ℏ " means "is an eigenstate of jz j z with that eigenvalue", then the π π state is linearly independent from σ± σ ± in definition 2. – ACuriousMind ♦. Aug 25, 2016 at 13:21.
Historically it was very successfull to start with a classical picture to get e good theory of the quantum world. It gives us something which makes it easier to interpret the quantum observables. If a quantum theory emerged through quantization of a classical one in a well defined way one has reason to hope that it would be easier to understand ...
In practice (first) quantization refers to describing particles as waves, which in principle allows for discrete spectra, when boundary conditions are present. The electromagnetic waves behave in a similar fashion, exhibiting discrete spectra in resonators. Thus, technically, quantization of the electromagnetic field corresponds to second ...
The answer(s) to your question(s) could easily fill a book (and in fact have). In short, quantization is a heuristic procedure that, given a classical system (Usually taken to be a Lagrangian or Hamiltonian theory of particles and or fields), produces a quantum theory (A Hilbert space and a Hamiltonian operator, more generally time evolution or even a unitary representation of the Symmetry ...
2. Energy is actually not always quantized in the sense of being discrete ;-) True, quantum theory does not invalidate E = mc^2, but you can only conclude that mass is quantized if you do the math for a particular particle at rest and find that it has discrete bound states. (By the way, it's E^2 = m^2c^4 + p^2c^2 in general) – David Z.
1. For the most famous speculation about quantization of charge, a search term is Dirac quantization condition. – rob ♦. Oct 18, 2021 at 3:52. Add a comment. Thanks for contributing an answer to Physics Stack Exchange! Asking for help, clarification, or responding to other answers. Making statements based on opinion; back them up with ...