Well, some quantum problems  have no clasical equivalent, so it is hard  to

answer this question. When there is some correspondance one might say that

Poisson brackets become operator commutators. Luck with this.

I'm not sure what you mean by "quantum strategy" but I will say that all quantities rendered in quantum equations can be applied to classical situation so long as the Planck constant is used to quantify the discrete quantum jumps. An example would be in calculating momenta.

Yes, what is "quantum strategy"?

BTW, there are no "discrete quantum jumps" as all quantum transitions are continuous, see Schrädiger 1926

That is correct. They are continuous.

It depends.

See

https://www.researchgate.net/publication/284350911_Strategia_resenia_otkrytyh_zadac_i_asimmetria_vrasenia_vokrug_tocki_vpravo_i_vlevo

Article Стратегия решения открытых задач и асимметрия вращения вокру...

What means "quantum strategy" is not clear to me too.  

There are much more parts of quantum theory which can be understood classically than usually presented.  Most of them are used in realistic interpretations like de Broglie-Bohm theory, Nelsonian stochastics or Caticha's entropic dynamics.  They all have a trajectory q(t).  Part of the Schroedinger equation is simply a continuity equation for the probability flow.  The other part is essentially the classical Hamilton-Jacobi equation, only with an additional quantum potential.  

I amend my answer. Events are continuous or discrete depending on the way we measure and what we pay attention to analogous to the way that digitized information can appear to be analogue information  but is still made up of discreet units (quanta).

thank you very much, I'm excited and also agree with your suggestion, Your answers were perfect. 

Dear Amirreza

All the fundamental equations of quantum mechanics (Schrödinger, Dirac, etc.) are derivable classically. To do so, simply enter the random action of the Planck’s vacuum through the probability density, and then follows classical mechanics. The number of works exploring this suit is too big, and the results are all conclusive [de la Peña L., Cetto A. M., Hernandez A. V. The Emerging Quantum: The Physics Behind Quantum Mechanics, Springer, 2015.]. In this sense, all phenomena are classical. Nevertheless, the randomness of vacum induced fluctuations, in one way or another, is inherent in all of them (gauge invariance of physical laws have the power of explicit it). Some seem to have no classical equivalent, but this should be viewed as a competition of several elementary phenomena generating a complexity, and not as a new universal order.

There is no derivation for Schrödinger, only plausible arguments.

Dear Juan

I respect your position (you is not alone), but “plausible arguments” is too vague when taking into account the contingence of the crescent number of theoretical and experimental facts, which support the idea that quantum mechanics describe vacuum induced fluctuations (random periodical movements compatible with a wave equation).

If not, what is the phenomenological origin of quantum mechanics?

We must be careful; the beauty and the precision of the quantum formalism — synthesizing intricate classical phenomena — is contagious.

 https://www.researchgate.net/publication/284350911_Strategia_resenia_otkrytyh_zadac_i_asimmetria_vrasenia_vokrug_tocki_vpravo_i_vlevo

Article Стратегия решения открытых задач и асимметрия вращения вокру...

Dear colleague

quantum mechanics is considered as an axiomatic theory based on purely  mathematical rules. It was first introduced as a non-relativistic theory . There is still a difficulty in understanding the connection between mathematical tools and the physical interpretation in quantum mechanics . Also, the appearance of the constant ħ (Dirac constant) in the Schrödinger equation is considered as one of the mysteries of quantum mechanics . Another mystery is the wave nature of the solution to the Schrödinger and other relativistic quantum mechanical equations. This wave nature is axiomatically connected with the non-classical probabilistic behavior of quantum systems in analogy with the electromagnetic wave of classical electromagnetism and its connection with the probabilistic nature of photons in light fields with some differences.

The quantum results in macro-physics system is completely corresponding with classical results, but in micro physics system , there are many differences between quantum and classical mechanics like stability of atoms , photoelectric effect, production of pair, ...ect .

Regards 

Effective advancements of the physical knowledge require phenomenological descriptions of the electromagnetic-quantum-relativistic behavior of massless elementary electrical charges. This only will happen when the background of radiation (half-quantum), evidenced by Planck in his second radiation law, be treated as a fundamental interacting environment where physical laws takes place. By the way, a theory of everything must have an “absolute” referential.

Fernando, others

There is a trend to say that QM is due to a very small scale

violent rattling effect, considering also the wave function due to

a physical effect (David Bohm and others), but this is still a very

minority position.

Regards, Juan

Bohm's theory simply substitutes particle states by an ensemble of trajectories, which are randomically occupied by particles during a very short time. The merit of the theory lies only in partially evidencing the phenomenology inherent to the Schrodinger equation (there is implicit a complex diffusion equation). The practical aspect, compared with the traditional quantum mechanics, is easily disputable. Notice, Bohm's theory at no time introduces vacuum-induced fluctuations (Planck's vacuum) to justify the complex diffusion equation (random jumps between trajectories); all interpretations emanate from the simple decomposition of the Schrödinger equation into an equation accounting for an ensemble of trajectories (Hamilton-Jacobi) ), on which the particle bounces according to the complex diffusion.

Article Addendum to “Phenomenological Derivation of the Schrödinger Equation”

Fernando,

Interesting ideas! 2 questions:

i) Assuming P to be real-valued (see, eg, (10), (13) looks strange.

ii) |grad psi|^2 = -psi* grad psi below of (14) is certainly a typo.

Best wishes,

Peter

Despite claims of derivation, it is imposible to distinguish acepted Quantum Theory, from a multiple of close cousins, who give the same results of QM in some given limit.

For example any number of new terms can be added to

Schrödinger and you would never know if they might arise in some new situation.

Then pseudo hermitian QM contains ordinary QM as a special case and it is in fact more general. Then you cannot prove that

Schrödinger is the only admisible answer.(or Dirac)

QM is like some open game which adapts itself as time goes on

to explain some very strange behaviour.

Christian,

You should first disprove the work by Dieter Suisky and myself before claiming "There is no derivation for Schrödinger, only plausible arguments."

Best wishes,

Peter