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# Concepts that Changed from Classical to Quantum Theory

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During the first three decades when quantum theory was being developed major new concepts that emerged were as follows.

1.  Discontinuous nature of physical process} such as emission of radiation in Bohr model absorption of radiation in photoelectric effect.
2.  Quantization of physical observable quantities}, for example angular momentum and energy in Bohr model.
In  quantum description, the dynamical variables are quantized, in general, they can take only some discrete values.
3.  Wave particle duality was an important change in concepts that brought in major changes in the way we think of physical system. The fact that in quantum world both matter and radiation have dual nature had far reaching consequences. However, It must be remembered that the two natures are complimentary and do not manifest themselves in any single experiment ( Bohr complimentary principle)

In addition to the above mentioned changes, the quantum theory brought many new concepts and forced revision of several classical ideas. We recapitulate  some important classical concepts  which underwent a complete revision after the quantum revolution.

• Principle of superposition of states  in quantum theory has a very different nature  as compared to the classical theory.
• In classical theories there is no restriction on simultaneous measurement of a pair of variables.
Unlike classical theories, a generalized coordinate and canonical conjugate momentum can not  be measured to arbitrary accuracy simultaneously. In  general two arbitrary dynamical variables cannot be measured simultaneously.
• The classical theories are deterministic, once initial state is specified the  motion of the system is deterministic; out come of any measurement can be predicted.

The quantum theory is  probabilistic; state has only probabilistic interpretation; only probabilities of different possible outcomes of experiments can be predicted by the theory.
• In classical theory we  associate a well defined trajectory with motion of particles. Waves are not localized and one cannot associate definite trajectories with waves. Properties of particles and waves are incompatible properties. In quantum theory every system exhibits a dual nature.
• The classical motion of particle is confined to regions where the total energy is greater than the potential energy. A particle cannot cross a region where the potential energy is higher than the kinetic energy.
A quantum particle can tunnel through a barrier, as is the case in alpha decay.
• In quantum description identical particles can not be distinguished, they loose their identity.

Our understanding of  classical concepts requires a major shift, or even a complete change. In addition many new concepts are brought in by the quantum theory.

In addition entire mathematical framework needed for description of quantum phenomena changes. While the mathematics prerequisite for classical mechanics for solution of problems is differential equations and partial differential equations, quantum mechanics brings in Hilbert spaces and probability theory in an essential way.

Also note that the kind of questions that are meaningful for a classical system, do not all remain valid questions in quantum mechanics. For example, for a classical point particle we may ask for its position and momentum at different times but not  for a quantum particle ( which is also a wave ). There are a whole host of new physically meaningful questions that are not asked in the classical physics.

You  understand all this more clearly as you move on and learn the subject. Before moving on, I leave you with a quote from the quantum mechanics book by Landau and Lifshitz:

Thus   quantum mechanics occupies a very unusual place among physical theories; it contains classical mechanics as a limiting case, yet at the same time it requires this limiting case for its own formalism.''

Think about the statement that Landu and Lifshitz make about `intriguing' relation between the classical and quantum theories. Learn more from the original source.

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