Yes, because the Schrödinger equation doesn't describe the motion of a particle in a medium, but the space of states of a particle, for instance, in a medium.

“Is Schrodinger equation is valid for all media and particles moving in it?”

- it can be valid - if it can be written correctly…

Cheers

Hi, thanks for the answers, as I understand the effect of difference particle/or medium is embedded to wave function so the formulation is generic but the wave function differs wrt to particle or medium, and as Stam Nicolis said "but the space of states of a particle, for instance, in a medium" states are differs according to the particle and medium difference at least at the level of pdf of wave function if they are not exactly the same particles excluded small perturbations.

And then a new question arises how is it possible to write accurate probability distribution function if the wave equation has many (may be near infinite states) how to measure each state and make a statstic and write a true pdf for it. Even it may be not possible because the reality of the measurement inability you may said start a predicted prior and use such bayesian technique and update the pdf with new data may be possbile but not exactly accurate....Thanks

The Schrödinger equation was initially conceived by him to account for the integer related sequence of resonance volumes corresponding to the possible orbitals that the electron visits in the hydrogen atom in relation with de Broglie's discovery of this resonance sequence as described in his 1924 thesis.

The probability distribution function is an add-on method developed by Heisenberg that maps over the volumes defined by Schrödinger's equation, and Feynman's later addition of the path integral method is a third method also meant to map over these volumes.

Its application to other volumes came later by similarity.

Put in perspective in this article:

Article An Overview of the Hydrogen Atom Fundamental Resonance State...

“…new question arises how is it possible to write accurate probability distribution function if the wave equation has many (may be near infinite states) how to measure each state and make a statstic and write a true pdf for it.….”

- really this new question in quite most cases isn’t interesting in physics, just because of in such cases, while it is quite physically clear that many QM objects and states are involved, it is quite clear also that really exact description and experimental investigation are impossible practically.

Correspondingly the complex systems are studied in mostly Applied Physics, where some approximations that don’t affect just physics are used – a typical example is electronic shells of large Z atoms, which are calculated using, say, Hartree–Fock, etc., approximations; etc..

In just physics just mostly simple, and so rigorously enough defined, objects/systems are studied, where the discovered/ring physical links/laws/constants can be measured with high enough precision, and have certain enough ways of interpretations.

Cheers

There is no single equation exist to describe nature such as wave.

The waves in nature is three dimension that constantly changing through temperature and pressure, while equation is one dimension, static, does not recognize temperature and pressure.

sorry

Hi, thanks for the answers. This question is a spare time think-tang and from not an expert physics graduate and sorry for English errors.

As Sergey quoted: " In just physics just mostly simple, and so rigorously enough defined, objects/systems are studied, where the discovered/ring physical links/laws/constants can be measured with high enough precision, and have certain enough ways of interpretations. " the simple systems such as Hydrogen atom may be modelled very finely but when the complexity of the system augmented (such as molecules in a excited from an outer source such as EM radiaiton, vibration, heat...) than it becomes hard to both model and predict the system state with high accuracy because the uncertainty even low for each parameter it is increased by the complexity of the system so cause to decrease of the system state predictability, I think.

As Preston Guynn quoted: "Look at that "near infinite states" as assurance of a career full of work reverse engineering QM equations from the experimental data, or study and apply", it may be very interesting but my knowledge about it limited at least now, for example if the states are linear and observable then it may be possible though the possiblity is still low, but if the states are not linear and directly observable such as the observable one may be the product of a back (hidden or unhidden) combination of states and operations and if the number of back step and parameters increase then my today physic knowledge is not enough to accurately predict it, may be later it is more possible with new knowledge, processing capacity and .... But I supposed it is not necessary to completely formulate the exact state distribution such as "the gas in a room may be collected at a certain place has a probability according to QM" (my physics lecturer said in BS, Y.Yılmaz) but in reality it is not necesary to calculate it.

And as Javad Fardaei quoted: "The waves in nature is three dimension that constantly changing through temperature and pressure, while equation is one dimension, static, does not recognize temperature and pressure."

I did not examine the wave and temperature, pressure relation but I think they could be embeded to the wave equation if the wave and these parameter relations are known well but as i qutoed above if these or other paramters relation are not well known for example at a certain temperature and pressure the wave equation has two or more different outcomes then it is hard to relate directly or place these parameters to the exact postion in the wave formula, but this case may also be formulated as QM wave equation in a probabilistic manner (but the accuracy also changes as narrated above).

Thanks for seperating time for answering.

Baris, you write

“…the simple systems such as Hydrogen atom may be modelled very finely but when the complexity of the system augmented (such as molecules in a excited from an outer source such as EM radiaiton, vibration, heat...) than it becomes hard to both model and predict the system state with high accuracy because the uncertainty even low for each parameter it is increased by the complexity of the system so cause to decrease of the system state predictability, I think…”

- it seems it is worthwhile in this case to repeat what is in the SS posts above: “In Just physics just mostly simple, and so rigorously enough defined, objects/systems are studied, where the discovered/ring physical links/laws/constants can be measured with high enough precision, and have certain enough ways of interpretations. "

- while, again, that in your quote really relate only to Applied Physics, which principally works in framework of “Just Physics”; and the problems that you point in the quote aren’t physical, but are technological ones; while in this case practically nothing new and useful in physics . really can be obtained.

Cheers

Hi Sergey, I suppose I understood your point of view, of course for the serenity of mind simple physics is enough to understand, interpret and implement it, but if someone connects physics or any other science with the philosophy of the life, as x science or total science is enough to define all the whole things in real life, then the definition not complies with the reality as I try to understand and comment above with the words of physics, such that if almost 99.9% of an elementary part of the system is well known, this knowledge is a good starting point and very effective in low dimensions or large dimensions, but I think it is not successful to define the more complex system than itself when the number of parameters, the uncertainty of measurement,... and the possible contracted hidden stages make the exact modelling very difficult in terms of complexity and formulation wellness of the system.

And with the new era of ai it may be more possible to observe, detect the unknown patterns or formulations but I also supposed that it will be not possible to create a real apple on the table even if whole scientific knowledge and power of the technology come together fully complied with each other, excluding magic and unreal one or a help from the heaven (according to my today knowledge). Greetings.

The validity of an equation in physics always has, for the lack of a better term, a "time limit" on it since a "theory of everything" has not been achieved so far. When you dig deeper, there will always arise effects which may require additional considerations and corrections.

Now, you mentioned glass, water and air as examples of matter. For these, the Schrödinger equation with a properly constructed Hamiltonian can reach down quite far and explain quite a lot, although analytic solutions are not available and we are forced to rely on computational, approximate solutions for the states of the electrons in them.

However, the Schrödinger equation is pure Quantum Mechanics and does not intrinsically contain relativity. You can add terms to it to make it "relativistically corrected", but that is not a definitive solution. There are valid approaches to unify QM with special relativity, but if you dig down so far that general relativity starts to matter, things turn sore pretty quickly.

I would say that this is a mountain to climb, but basically every mountain on earth has been climbed while this problem hasn't.

It is actually a quite common, some would call it "mainstream", saying that theoretical physics is sort of "stalled" in this respect because, while there are deeper concepts to replace the current equations, there is no clear strategy for verifying these.

So, until someone comes around with something that's globally better and not just for selected effects, we're stuck with the Schrödinger equation, but the results it provides have been quite good in the past 100 years, so we could be off worse.

That

“…The validity of an equation in physics always has, for the lack of a better term, a "time limit" on it since a "theory of everything" has not been achieved so far.….”

- is, of course, in principle, correct, though the term "theory of everything" in mainstream physics is rather official one, and means “unification of all fundamental Nature forces into some one Force”. What is fundamentally wrong, the Forces are fundamentally different and really there is no any necessity in some “unification”.

Though Matter indeed is rather simple logical system that is based on binary reversible logics that is “materialized” in the Matter as that absolutely everything in Matter is/are specific disturbances in the Matter’s fundamental, universal, and 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], the lattice is placed in the corresponding Matter’s 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);

- while, as that is rigorously scientifically shown in the Shevchenko-Tokarevsky’s 2007 initial model of Gravity and Electric forces

https://www.researchgate.net/publication/365437307_The_informational_model_-_Gravity_and_Electric_Forces

- and 2023 initial model of Nuclear [that binds nucleons in nuclei] Force https://www.researchgate.net/publication/369357747_The_informational_model_-Nuclear_Force ,

- all these Forces [and it looks as quite rational to assume that Strong force that compose hadrons also] act by the same one scheme – i.e. act in 3D space, the Forces mediators fundamentally at least at statics don’t contain/carry energy, while all Forces mediators are some “rims” in the lattice, which are radiated by fundamentally different Forces charges, propagate in the lattice with the speed of light, and cause/trigger releasing of elementary momentums p=±ћ/r, r is distance between “radiating” and “irradiated” particles, which attract/relapse these particles. The difference of Forces’ strengths is determined only by intensity of radiating rims.

Nonetheless despite these common points in Forces, the Forces, again, are fundamentally different, including, first of all, are different functionally; just so everything in Matter is as it is.

However if that doesn’t relate to the "theory of everything" official meaning, really this theory is principally formulated and works in physics more 200 years already, though not correctly in some cases, but that is inessential in this case – that is classical and quantum mechanics, where now all Forces are well united as different potential energies U-parts in mechanical equations.

That is another thing that the equation in mainstream physics have fundamental flaws, see the links above and at least section “ Conclusion” in https://www.researchgate.net/publication/355361749_The_informational_physical_model_and_fundamental_problems_in_physics.

However that

“…However, the Schrödinger equation is pure Quantum Mechanics and does not intrinsically contain relativity. You can add terms to it to make it "relativistically corrected", but that is not a definitive solution. There are valid approaches to unify QM with special relativity, but if you dig down so far that general relativity starts to matter, things turn sore pretty quickly. …..”

- isn’t correct in some points. Schrödinger equation approach, i.e. using Hamiltonian operator at calculation of wave function and values of parameters of concrete physical systems, for electron was "relativistically corrected" by Dirac yet in 1928. That is another thing that, as that is shown in the last linked paper above really instead the Hamiltonian operator at least in time-dependent equations, the whole momentum operator, which doesn’t exist in mainstream QM, should be used, etc., more see the link

Cheers

As I said earlier I am not very expert on physics but that much I know today still it may not possible if someone considers all parameters and relations to be able to find an optimum solution for a problem that satisfy everytime it is the global optimum one (if the system quantizable). And I think if the number of paramters, relations and hidden operations come to the table it may go more harder to solve with today's knowledge and technology such as entangled particles which you have only one chance to measure their states (and that mcuh I know it depends to measurement method, in short it may effect the system), whereas their non-collapsed quantum states and further the non measurable but having effect on the system things. May be some day human can formulate their knowledge but I dont know when it is possible?