What are the benefits of quantum mechanics over classical mechanics?

Answer 1

Well, that depends on what you meant by "benefits". Either way, both of them have their limitations. Classical mechanics can not be used to accurately describe an atom. Just as quantum mechanics would be useless if you were asked to find the terminal velocity of a Baseball. Both areas have give us a plethora of inventions and technologies that would not have existed otherwise. Now in terms of learning the topics, quantum mechanics is deemed by some to be more interesting because of its mystery (probabilistic predictions) versus classical mechanic's seemingly dry Hamiltonians and Lagranians. Both topics are very powerful tools that are used to solve complicated problems, and one is not really better than the other but I believe that neither is complete. I hope that helped.

Answer 2

A few main differences:

1) Classical mechanics assumes that certain physical quantities -- such as charge or light energy or angular momentum -- can be reduced to an infinitely small level. For example, CM assumes that there is no level of angular momentum below which a particle can not go.

QM, on the other hand, states that there ARE certain levels of these quantities, below which they can not go. There can be no amount of charge smaller than the electron charge. The energy of light at a certain frequency can not be smaller than the product of that frequency and Planck's Constant ('h'). And a particle can not have less angular momentum than h over 2pi. There are innumerable other examples of quantized physical quantitites.

2) CM assumes that, IN THEORY at least, one can predict the final result of an interaction knowing enough of the initial conditions with enough precision. For instance, if one knows the initial speed and direction of a kicked football, as well as the atmospheric conditions, one could calculate the exact place where it will land. Similarly, CM assumes that one could know where an electron will land on a detector once it has left the electron gun and goes through one of two slits.

QM assumes that it is not possible to do this for small particles EVEN IN THEORY. In contrast, QM states that one can only describe the PROBABILITY of a small object ending up at a certain place. It is NOT the case, says QM, that we lack cleverness or good enough instruments -- it is that lack of precision is an inherent fact of our Universe.

3) CM assumes as "obvious" that, if an object goes from one state (say, an electron orbit of one Bohr radius ('Rb') from the nucleus) to another (say, an electron orbit of distance 2Rb from the nucleus), that object MUST have, for some period of times, been part way between those two states.

QM states that this transition occurs instantaneously, with that object spending zero time part way between these two states. In the example above, an electron can go from an orbit at distance Rb from the nucleus to an orbit at a distance 2Rb from the nucleus, without EVER having been at a distance of 1.5 Rb from the nucleus.

Werner Heisenberg once quipped (something like), "If you aren't bothered by the implications of quantum mechanics, then you don't understand it."

Answer 3

Quantum mechanics provides a more accurate description of the behavior of particles at the subatomic level, including phenomena such as superposition and entanglement, which are not accounted for in classical mechanics. It also allows for the explanation of diverse physical properties, like the discrete energy levels of atoms and the behavior of electrical currents in superconductors. Additionally, quantum mechanics forms the basis for many modern technologies, such as semiconductors and quantum computing.