The wavefunction has nodes; but what matters is the probability density.

There's nothing any more confusing about the probability density of the properties of a system in equilibrium with quantum fluctuations than about the probability density of the properties of a system in equilibrium with any other bath of fluctuations.

Preston Guynn ,

Almost all chemistry students have been taught this thought experiment probably for more than 70 years doesn’t matter if we like it or not understand or not understand. Many physics students were also taught with these experiments as far as I know and many of them will start with the harmonic oscillator, a more realistic model.

I personally do like this thought experiment only thing is I don’t like the solution. It is actually a good model for open-up spin, not for vibration. If you connect left to right, it is a free spin problem. Since the solution is consistent with the energy levels of the Bohr hydrogen model, I suspect the quantized Bohr energy is from quantized electron rotation rather than the quantized radial orbitals. Its results also have many practical applications in chemistry and photonics such as conjugated pi-electron systems in organic dyes and various quantum dots given surprisingly precise predictions of the energy levels.

Jixin

Dear Prof. Chen,

This is a very interesting question. We tried to answer it in a trajectory-based way. Perhaps our study could present a different perspective to this question. Please read

Article Trajectory Interpretation of Correspondence Principle: Solut...

Best Regards

Shiang-Yi

Dear Prof. Shiang-Yi Han ,

I agree with you that using random trajectories to reconstruct a probability density function is indeed complementary to the interpretation I proposed for a single trajectory with uniform energy density distribution with many allowed phase shifts. I hope it is now the right time for many of us to challenge the established interpretations from different perspectives and angles.

Jixin

Preston Guynn ,

I agree with you that we should be teaching the students true science but unfortunately, a textbook if exist covers the properties of electrons you have mentioned and is commendable to probably none chemistry students maybe some chemistry professors. And we have a huge need in chemistry to use quantum chemistry to explain and predict optics, interactions, and reaction mechanisms in the "technical" way you have mentioned which is a more common engineering solution than a science solution. It is the most computationally intensive process in the entire chemistry field such that Google and IBM's quantum computer projects both target this application. And unfortunately, we don't have enough professors to teach quantum so somebody like me who has been trained with these thought experiments and textbooks has to take the task. Quantum is also required by some engineering students and how many do you know that knows the topics you have mentioned?

I personally have no training and no idea of particle physics neither has the ability to develop teaching modules that include the fundamental part of the problem you have mentioned. We have been using textbooks developed by many chemistry educators and researchers which as you have commented a technical solution for fitting experimental data rather than a fundamental true bottom-up understanding of nature although you can see we think it is kind of bottom-up. Even if a such theory has been developed somewhere, it has to be accepted by the "mainstream" which is the majority group of us before being taught to the students which is an association agreement involving tens of thousands of researchers over the world. Also can the theory you have mentioned predict the energy level and color of a very simple molecule such as benzene? The particle in a box model with a proper reference point can.

In fact, there is a crisis in the entire higher education to find enough people who are interested in learning and teaching these courses given there is limited research interest and funds in the fundamental side of quantum chemistry and poor reward for the professors to teach these courses probably close to minimum pay salary. There are certainly much more interest and funding in the application side of quantum chemistry especially since the pharmaceutical industry has picked up the method in predicting drugs.

Many chemists including me have no problem in using or teaching pure engineering solutions such as artificial neural networks which have nothing to do with the physical nature of the matter.

dear Jixin Chen give me one reason that quantum mechanic exist.

When we call quantum, it means the interaction under atomic size, which to this date nothing of inside of atom ever confirm, such as electron/positron, proton/neutron, quark etc.

In other hand, all the quantum computer systems are talking about over the atom size. again chemists, engineering and medicine man are working over atomic size, nothing to do with quantum (inside) aspect of it.

To my understanding atom is the foundation (building block) of everything in our universe and it does not work mechanically to call it QM, as each atom act to temperature and pressure promptly to its nature.

Again to follow pseudoscience of modeling atom with electron is just elusion that science is practicing it with any reason for over a century.

. Deleted research item The research item mentioned here has been deleted

Dear Javad Fardaei,

Quantum as the name implies, describes an observation we have made to the microscopic systems you have described that energy is discrete rather than continuous, which is a typical phenomenon we see in resonated wave systems at the macroscopic scale. Other than this, there should be no difference from the classical mechanics you and I have learned to describe the observations we have measured or others have measured and we trust their measurements. You can call it wave mechanics if you like whichever name does not matter.

Then you use the theory to calculate something that matters to you, for example, the color of a compound you have synthesized, the melting point of a material, and the reaction of a few molecules which may happen to be drugs to cure a disease. So we slowly build confidence and faith in the theory until one day we are tired of its difficulty to understand, the cost to use a super-computer to calculate a simple molecule, and accuracy problems that always exist for even the best theory we have invented. Then it is time to seek a theory you think will work better in any of the aspects or other aspects not mentioned.

Dear Prof. Chen,

Yes, I agree with you. It is time to do something in different perspectives. Random trajectories is one way to view the trajectory interpretation of quantum mechanics. The key point is that the complex dimension extension makes it become possible to solve the probability noddle issue. We show how complex random trajectories can form the quantum compatible and classical-like probability distributions in the following work:

Article Extending Quantum Probability from Real Axis to Complex Plane

Best

Shiang-Yi

Dear Javad Fardaei

I think there are some misunderstandings here. We cannot say that quantum mechanics exists or not, because it is an empirical theory established by some great scientists. It proposes a kind of description to the quantum world. Not only atom be considered, in fact, some macroscopic phenomena can be found in the quantum world, such as superfluid, BEC, and so on. Scientists try very hard to deal with complex quantum system such as quantum chemistry. And some scientists and quantum engineers try to design and implement quantum computer which combines quantum mechanics and high technology involving many fields. On the other hand, some scientists working on describing biological phenomena through some quantum properties, like Nottale and his work:

Preprint Progress in Integrative Systems Biology, Physiology and Medi...

Indeed, we need some theories which can unify different theory in different scale and space-time. Any efforts people try to do on this road all pave the way to the next generation, right?

Shiang-Yi

“…In quantum mechanics, the Schrödinger equation calculated wavefunctions with a wave structure over space and changing over time. The Copenhagen interpretation, namely Born‘s interpretation states that the square modulus of the wavefunction represents the probability density function of the particle over space and time. Thus, there will be a distribution of the particle over space because we know particles are moving in the system and may favor some locations…..”

- yeah, that is indeed so; and that

“…..This is a very confusing explanation that several founders of Quantum Mechanics including Schrödinger himself, Einstein, and de Broglie have formally expressed disagreement. …..”

- is also so in that the Born‘s interpretation is really a vague transcendent one, since hasn’t some rational grounds/rational explanation - why that is so? However besides Copenhagen interpretation in mainstream physics there exist a number of other interpretations, which evidently look as more vague/transcendent – up to evidently fantastic “Multiverse interpretation”.

That happens because of in mainstream philosophy and sciences, including physics, all really fundamental phenomena/notions, humans directly interact with which - first of all in this case “Matter”, “Consciousness”, “Energy”, “Inertia”, “Space” , “Time”, “Information”, are fundamentally transcendent/uncertain/irrational; so, including, everything in Matter – particles, fields, bodies, etc., in physics really are transcendent, including because of this transcendence in QM the “interpretation problem” till now is solved as it is “solved” above.

All these phenomena/notions can be, and are, rigorously scientifically defined only in framework of the philosophical 2007 Shevchenko-Tokarevsky’s “The Information as Absolute” conception, recent version of the basic paper see in

https://www.researchgate.net/publication/363645560_The_Information_as_Absolute_-_2022_ed

- and more concretely at application to Matter in the in the SS&VT informational physical model 3 main papers are

https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics,

https://www.researchgate.net/publication/355361749_The_informational_physical_model_and_fundamental_problems_in_physics, and

https://www.researchgate.net/publication/369357747_The_informational_model_-Nuclear_Force , where, including, the quite rational initial model of “particles” and 3 “fundamental Nature forces” [Gravity, Electric, and Nuclear] are developed.

Particles are specific cyclic disturbances in Matter’s ultimate base –the (at least) [4+4+1]4D dense lattice of primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE], which compose the lattice; the lattice is placed in the Matter’s corresponding fundamentally absolute, fundamentally flat, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct); “FLE size” and “FLE binary flip time” are equal to Planck length and Planck time.

More concretely particles are some algorithms that always constantly cyclically run basing of “FLE hardware” as sequential “FLE-by-FLE” flipping in the lattice, which propagates in the lattice – and, of course, in [observed universally] 4D space metrics (at least) (cτ,X,Y,Z), along 4D “helixes”, the front of which moves in the space with 4D speed of light, having momentums P=mc [“bold” means 4D vector] and energy E=Pc=ћω, ω is the frequency the algorithm ticks with.

Correspondingly at every time moment a particle exists as the “particle-point” that has size ~ Planck length, and just that, i.e. that particle can interact by some fundamental Force also with other “particle-point” – since the Forces act mostly in 3D “space point” - means that “ a particle is in a 3D space point”,

- i.e. any particle really at every given time moment isn’t “distributed over space”, but at concrete interactions by a concrete Force with other particles can be in a concrete space point with some probability, which depends on the Force’s strength and some other physical effects, and this space point randomly can be in some 4D helix point,

- really in a space volume that has size ~ Compton/de Brogile length; and this probability distribution is described by corresponding Schrodinger equation if particles’ lengths are well larger than the Compton length, or, say, by Dirac’s equation for electron if the electron’s Compton length ~/> the de Brogile one.

More see the papers that are linked above, SS posts in

https://www.researchgate.net/post/H_denotes_the_constant_ratio_E_f_Ehf_is_it_possible_that_h_has_an_equation_both_without_E_and_f/1 and

https://www.researchgate.net/post/No9_Is_the_spin_of_an_electron_really_spin/3are relevant in this case as well.

Cheers