That's a good question, because it includes the matter of whether QM is explained/taught to a beginner, or to some graduate student.

On a beginner's level, from my own experience, I would recommend teaching the way Sakurai introuced it: starting axiomatically, but using a simple 2-level (e.g. spin-1/2) system, to get an easy understanding that all is about linear algebra. The easy math involved helps greatly to understand the basic rules of QM.

On a graduate level, i.e. when a certain level of understanding has been reached, I would surely recommend introducing the history how QM has been "found", because it greatly contributes to an understanding how new science is created, and how theories get born and developed. Apart from that, it really is a great story.

I would normally not recommend starting with a more rigorus mathematical approach. I am not sure if the details around the functional analysis of Hilbert spaces and even distributions do not blur the physics behind all this.

Best regards

Oliver

The related topic should be covered Hundts rule of maximum spin multiplicity ,

Spin orbit coupling .This is the classical part I think .

Thank you Prof. Tennert for your esteemed views and opinion .

Thank you Prof. Datta for your esteemed opinion and invaluable suggestions.

Dear Debopam Ghosh, you are welcome. But just to be honest: I am not a professor...

Best regards

Oliver

My Professor once told me that in academics we should always address our peers and colleagues regardless.I respect him deeply try to follow his advices the best to my abilities.

Thank you again Oliver .

I am not also professor , I shall

be very cordial with my name only .

Best wishes ,

Jaydip

duly noted Jaydip.

You are welcome I am also a learner of Quantum Statistical Thermodynamics .

You do not teach it directly, only after some modern physics coure that takes them

through most of the relevant experiments that started this off. If one likes this is historical.

Thank you Juan Weisz for your esteemed opinion.

Dear Debopam Ghosh ,

In my personal opinion, the traditional way of starting with the historical development of the subject - Quantum mechanics, followed by wave mechanics approach (being a very interesting story in itself), usually draws the natural curiosity and attention of the student, which is a great deal. Instead of replacing this method, if I were in that place, I would then continue to the axiomatic introduction to the subject, followed by discussion on Quantum mechanics of spin ensembles approach.

Thank you Lalitha Nallamothula for your esteemed opinion.

Teaching QM ? Every failure in didactics reveals a failure in conception. The examples are many, alas.

Let us begin with a reference: Insights into teaching quantum mechanics in secondary and lower undergraduate education, (21 pages) issued in PHYSICAL REVIEW PHYSICS EDUCATION RESEARCH 13, 010109 (2017), by K. Krijtenburg-Lewerissa, H. J. Pol, A. Brinkman, and W. R. van Joolingen, all four Dutch persons.

Link: http://journals.aps.org/prper/pdf/10.1103/PhysRevPhysEducRes.

13.010109

They acknowledge that to teach according to the hegemonic tradition, gives painful results. « the introduction of probability, uncertainty, and superposition, which are essential for understanding quantum mechanics, is highly nontrivial ». They point as guilty that all that is “counter-intuitive”, and point the “classical world” as the big in the wrong. They are not able to detect that if it is so difficult to implant into students not yet selected on their obedience and tolerance to absurdity, maybe the reason could be that the doctrine is silly and ill-conceived.

I have listed elsewhere some 21 surreptitious and clandestine postulates on which the standard teaching of QM is grounded. Many of them are anti-somebody postulates, for 1925-1927. Others are anti-experimental-corpus. Sure the formalism is correct, though unusefully obscure, as it is 100% undulatory and deterministic, but the semantics they teach before the formalism is pure delirium.

In its hegemonic form, the teaching of QM is like a knight in armour who have sent his horse alone across the river. Now the horse and the formalism are on the right side of the river, undulatory and deterministic, while the knight is still on the corpuscularist side, and he cock-a-doodle-dooes : "Nobody can understand Quantum Mechanics!  So I am the modern forever!".

Instead, the Transactional (Quantum) Microphysics relies on ten explicit postulates, published here also.

1. The absorbers and their properties exist. No “corpuscular aspects” exist.

2. Planck and phase postulate. The unit of phase or angle comes back in the dimensional monomial.

3. De Broglie-Dirac-Schrödinger postulate. If a particle has a mass, the intrinsic frequencies mc²/h and 2mc²/h play each one their role. The Broglian mc²/h for each interference of a quantic particle with itself. The Dirac-Schrödinger 2mc²/h for all electromagnetic interactions, for instance, the Compton scattering.

4. Fermat-Fresnel Postulate. For each individual wave, all the real journeys come in phase to the absorber, eventually at an integer number of periods (it is then an interference). Hence the geometry of the Fermat’s spindle between emitter and absorber ‒ several spindles in case of interference on the travel.

5. Every photon has an absorber. A photon is a successful transaction between three partners: an emitter, an absorber, and space or optical devices between them. This transaction transfers by electromagnetic means, a quantum of looping h, and an energy-momentum whose value depends on the respective frames of the emitter and the absorber.

The limits of this definition: One cannot quantize the acceleration of an electron in a magnetic or an electric field. So the acceleration of an electron in a vacuum tube, in a cathodic ray tube or in an electronic microscope, or in a particle accelerator, the synchrotron radiation, the Bremsstrahlung (braking radiation) all that escape to the quantic sub-domain: no stationary states with defined frequencies before and after. In the case where the boundary conditions are quantic, the transferred momentum is hν/c in the frame where the frequency ν is considered.

Corollary. As soon as you admit that the absorbers exist, pffuitt! These “Collapses of the wave-function-spreading-everywhere” lose any interest, and are only good for the garbage can of the History.

6. The properties of a crowd of individual waves flow from the properties of the individual waves, and not the inverse.

7. Macro-time ≠ micro-times. The god of Isaac Newton, in charge of all seeing simultaneously, does not exist. The time of Isaac Newton, a supposed universal and ubiquitous parameter, does not exist either. We distinguish the macro-time of macro-systems such as the laboratory, from the micro-times where dwell all the gropings of Broglian waves from which emerge the successful transactions. The macro-time is a local and statistical emergence, and it flows the same way as the entropy, a statistical emergence too. It has no causal properties in microphysics.

Corollary:

We cease to presuppose that the causal irreversibility proved in macrophysics for the macro-time could be extrapolated to the micro-times the transactions emerge from. This irreversibility is a crowd effect. We cease to disdain and censure the two retrochronous solutions resulting from the Dirac equation for the electron, or any fermion.

8. Kirchhoff's Principle of retrosymmetry.

In 1859, Gustav Kirchhoff proved that the Fraunhofer dark spectral lines from a cold gas or vapor correspond to bright spectral lines of the same elements in a hotter gas. So the spectral emission of a photon is exactly the same physical phenomenon as the absorption. Generalization: the retrosymmetry applies to the low energies of all the atomic physics, the molecular spectroscopy, and all the solid state physics.

Limitations: No experimental proof of retrosymmetry exists in the domain of nuclear physics, nor in the nucleosynthesis in the implosion of a supernova, nor in high energies. Where a neutrino is emitted, no retrosymmetrical experiment is feasible.

9. No, it is impossible to isolate a quantic system as we isolate its equations at the blackboard: No mean exists to shield the Dirac-de-Broglie noise. It is impossible to predict which transaction will emerge from this lapping, nor when. The implied de Broglie frequencies are inaccessible from our human scale, and the theorem of the requisite variety, from William Ross Ashby, is here to ruin all our fantasies of panoptical omniscience. Moreover, the innumerable involved micro-times are bi-directional: orthochronous and retrochronous.

10. Then the moral principle: we refrain from censuring the experimental results that embarrass the doctrine in power.

Hiding so many experimental facts to the students is wrong, and it violates the scientific deontology. Sure, so many experimental results embarrass the copenhaguists: All the spectral absorptions, all the interferences as the anti-reflective coatings, quarter-wave plates, interferential colors, the Goos-Hänchen effect in plane polarization, Imbert-Fedorov in circular polarization, all proofs of the non-negligible width of each photon. A very long list! They hid from you the transparency effect Ramsauer-Townsend, which is strictly undulatory. But if the electron is strictly undulatory, how will they continue to impress the gullible public, by their mystic “wave-corpuscle dualism”? Many other everyday experimental results are incompatible with the corpuscular ideation of the Göttingen-Københavnists.

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thank you Jacques Lavau for your esteemed and highly valuable opinion, and also for providing me some new directions into study of Quantum mechanics, i will definitely go through the references you have mentioned and try to better my own understanding in this regard.

Well, I would indicate reading the classical Max Jammer "the Philosophy of Quantum Mechanics", "the Conceptual Development of Quantum Mechanics" in order to make it clear for yourself a better approach to the nature of Quantum Mechanics. Reading about philosophy of Quantum Mechanics is very important for such task.

Around six years ago, there was a discussion on what kind of didactic sequence would be better to teach quantum mechanics, a dichotomy I would call "classical-like" and "quantum-like". The first ones would say that you should use classical physics as prior knowledge for introducing quantum mechanics, meanwhile the second ones would say classical mechanics would be an epistemological obstacle for learning quantum physics, so you shall avoid it. Both ideological groups pointed good and interesting results. Well, maybe nowadays the discussing may have changed, but searching for Physics Teaching articles would be interesting to reach a conclusion (seeking them with ERIC is a good start).

Dear Glauco Cohen-Pantoja

Thank you for your extremely valuable reply and suggestions.