# Posulates of quantum mechanics

1. Jan 15, 2008

### shalu

hai please tell me the posukates of quantum mechanics,
actually what they are stating,

2. Jan 16, 2008

### Bowles

3. Jan 16, 2008

### Marco_84

Often the postulates you find in some books/websites are redundant...
wich tells you that what usually are called the 1st,2nd,3rd postulates are not completely independent.

bye
marco

4. Jan 17, 2008

### shalu

thanks Mr.bowles i got it .
iam also confused eigenstates ,eigenfunctions

5. Jan 17, 2008

### waht

An operator when acted on a function can change it according to some rule. A derivative is an example of an operator.

If an operator operates on an function, and if the result spits out the same function multiplied by a constant number, then that function is called an eigenfunction, and the multiplier is an eigenvalue.

If you know some differential equations try this. If

$$D = \frac {d}{dx}$$

is an operator, and $$f(x)$$ is a function, and $$a$$ is an eigenvalue,try solving the equation

$$D f(x) = a f(x)$$

See what the eigenfunction is, and its eigenvalues.

Last edited: Jan 17, 2008
6. Jan 18, 2008

### peter0302

I looked at the "postulates" at http://hyperphysics.phy-astr.gsu.edu/Hbase/quantum/qm.html. My favorite is this:

In other words, the sixth postulate of quantum mechanics is that quantum mechanics is right.

7. Jan 18, 2008

### reilly

actually what they are stating,

There ain't none. QM is a phenomological theory founded on experimental data. However there is a pragmatic formalism that works pretty well, which can seduce some into thinking there is a way to formulate QM as if it were a bunch of theorems in Functional Analysis.

A challenge to those who think my statement is spurious -- Name a theory of physics that is fully formulated and described by postulates, axioms or stuff like that?

Regards,
Reilly Atkinson

8. Jan 18, 2008

### peter0302

Relativity.

9. Jan 18, 2008

### reilly

Regards,Reilly Atkinson

10. Jan 19, 2008

### peter0302

I'm not sure if you're being facetious, or if this is some kind of trick question, but:

Postulates:
1) Speed of light is invariant for all observers
2) There is no preferred reference frame

Those, along with definitions of velocity, force, acceleration, momentum, and energy, yield the most familiar parts of special relativity, including E=mc^2, and E=pc (without which, ironically, QM would not be possible to formulate). Most importantly, these formulas are totally derived from postulate, not formulated ad hoc through observation. They were only experimentally verified later.

11. Jan 19, 2008

### lightarrow

I assume you mean that physics is not mathematics: physics cannot come from "invented" ideas put as postulates even in a coherent theory, but is based on experimentally verified or verifiable facts and if those facts cannot be verified or until they are verified experimentally, that "theory" is meaningless. If you thought the OP could have a doubt on it, you did well to point it.

12. Jan 20, 2008

### peter0302

Based on how you describe it, physics is no different from mathematics.

Take the best known example of postulates forming a physical theory - Euclidean geometry. Euclid didn't just "make up" his postulates - he based them on what others and/or he himself had seen. He then formulated a physical theory of geometry that flowed logically from the FIVE SIMPLEST STATEMENTS he could make.

Isaac Newton and Einsten did exactly what Euclid did. The theories they came up with were hardly "meaningless" before experimental verification. They both fit all of the then known experimental data AND made new predictions which allowed engineering which hadn't been possible before.

Newton and Einstein came up with physical theories. So did Euclid. Their processes were exactly the same.

Quantum Theory is vastly different. There has been little to no success into boiling quantum theory down to more fundamental, simple postulates. The standard model, though it fits all experimental observations, is a mess. This is a theory that has taken the incredible experimental data that we have seen and drawn a circle around it. What irritates me is when physicists (notably those believeing in the Copenhagen Interpretation) tell us there is no value in looking for deeper, more fundamental levels of physical reality. The phenomological approach has unquestionably brought us great advances - but the logical approach should not be discouraged either! Ultimately, it is the logical approach that, I believe, will take us beyond the current roadblocks.

13. Jan 20, 2008

### Haelfix

"There ain't none. QM is a phenomological theory founded on experimental data"

I don't quite buy that. Non relativistic QM can be made into a fully self consistent axiomitized system mathematically. For instance via the path integral formulation with a well defined measure. The one hitch (unlike classical mechanics or relativity) is that one of the axioms deals not with kinematics or dynamics but with interpretational issues of what it means to observe something in the lab. However its not really a phenomenological theory *yet*, in the sense that you don't need, 'a priori' experimental input to fix any variable in the theory. Of course, when you do say atomic physics or things like that, it will require modeling.

14. Jan 20, 2008

### lightarrow

You mean that, as for geometry (changing of 5° postulate --> non euclidean geometries), if I arbitrarily change some of the newtonian "postulates" I obtain another classical mechanics as valid as the newtonian one? I hope you are not saying that seriously.

15. Jan 20, 2008

### muppet

To say that quantum mechanics has no postulates is wrong. The mathematical formulation of the theory has postulates that describe the behaviour of some "state", which Von Neumann took to be a unit vector in a hilbert space, and that relate this state to what we observe in a lab. You typically won't be explicitly presented these axioms in a normal physics undergrad course, but what the axiomatic presentation amounts to is the most concise possible statement of the entire lecture course. (Of course, simply being told the axioms wouldn't necessarily help you understand them brilliantly...)

16. Jan 20, 2008

### peter0302

As a matter of fact, if you change Newtonian mechanics slightly, specifically velocity transformations, you obtain Special Relativity, which is superior to Newtonian mechanics for speeds close to 'c', while Newton remains perfectly adequate for slower speeds.

Also, no mathematician just arbitrarily dismisses the Fifth Postulate and makes up something completely random. Any useful non-Euclidean geometries are based on physical observations too (i.e. General Relativity). Most non-Euclidean geometries are invented by academics who need tenure and are useless.

Anyway, these theories all work perfectly well in the median conditions and break down at the boundaries. As, incidentally, does quantum mechanics. These are different approaches. But to throw out logic completely is simply unjustifiable.

Last edited: Jan 20, 2008
17. Jan 20, 2008

### muppet

I'm not entirely sure that's true...
Chapter 2 of Penrose's "The road to reality" talks about the history of the developement on non-euclidean geometry. There he says that people first started to consider the possibility as a result of unsuccessful attempts to prove the parallel postulate by a reductio ad absurdum method. The first prominent, consistent expositions of non-euclidean geometries detailed there predate GR by about 100 years.

18. Jan 20, 2008

### peter0302

And how many of them proved to describe physical reality in any way besides GR? There's your difference between "making things up" and a well formulated physical theory based on postulate and logic instead of _mere_ observation of phenomina.

19. Jan 21, 2008

### muppet

Myresponse was intended to be to:
My point was that Non-euclidean geometries were developed completely without regard to physical observation as pieces of pure maths in their own right; to say that they are useless to a physicist is rather like saying that the theory of evolution is useless to a mathematician. It's technically true, but try telling people who work within the discipline of the theory that it's useless!

20. Jan 21, 2008

### lightarrow

I don't know now, but when I studied quantum mechanics for the first time at university (in Florence), they first gave the postulates and then an explanation of them. So, you can be sure I'm one of the first to think about QM as coming from postulates (independently on how this is correct or not).
But I agree with Reilly on the fact that too many people is not completely aware of the thin differences between physics and mathematics when they talk about QM, if this is what (I presume) he intended.

Last edited: Jan 21, 2008
21. Jan 21, 2008

### peter0302

And my point is that Euclid, Newton, and Einstein all did the same thing - started with simple postulates that, to them, represented the most fundamental statements they could make about the physical world. There is a difference between pure mathematical logic (which as you say is of no use to a physicist) and logical derivation of physical theory, which is of immense use. Einstein wasn't in it for mathematical curiosity - he was in it to discover the nature of the universe, and he came pretty darned close.

22. Jan 21, 2008

### reilly

I'm ferociously serious, for many reasons. Physics is about Nature, mathematics is about human thought patterns. Mathematics is the primary language of physics. Just as is the case with ordinary language, the language of physics has referents in Nature -- nouns like space, time, speed, electric charge refer to aspects of Nature -- they have no meaning without Nature.

The idea, for example, of a closed set, as one containing all its limit points is quite a different matter, just like the idea of of an integer or real number -- these all spring from the depths of our minds -- its not crazy to think that some of the basic ideas of math are ultimately empirical in nature. But math, to a substantial degree, is purely an exercise in abstract thinking with no reference to anything but the work of other mathematicians, with no reference to the natural world. Thus mathematicians are looking for internal consistency, upon which more consistency can grow -- although when the consistency is absent, a new math path might open up.

Physicists, on the other hand, are all about trying to figure out what's going in in Nature. Some are intensely pragmatic, others are extraordinarily abstract and abstruse. The plain fact is: Nature is not very orderly, and it's is full of surprises. Stuff changes, so why be overly shackled to some ideas that, in fact, might turn out to be wrong.

I have no problem in teaching QM, going from Planck to Bohr to modern QM, and simply making the Schrodinger EQ. plausible, based on a whole bunch of experiments, ideas of waves and diffraction, and contact transformation and Hamilton's Principle, which puts optics(eikonal) and mechanics into tantalizing proximity. Is there a problem with this way?

If physics can be axiomitized, then why was not QM invented before it was?

OK. Let's do relativity.

!., What is the speed of light? (Don't forget Faraday)

2. What is an observer?

3. What is a reference frame?

4. Where do the definitions you refer to come from?
What are they?

Einstein himself is a master at expressing some of my concerns about the importance of empirical evidence. His great papers of 1905 were all directly based on empirical concerns -- photoelectric, Brownian Motions,....--. In a sense his first SR is directly based on empirical evidence as well -- he cites Maxwell's Eq. Do read Einstein's monograph entitled Relativity. He goes to extraordinary means to explain space and time in terms that 1. we can understand, and 2. which dovetail in a very elegant way with his further discussion -- the train expt., etc.

I'm still far from convinced that you've got all the postulates you require. For example, do you not need to say something about the relationship or roles of humans and Nature? (See David Hume)

lightarrow has got it right.

Regards,
Reilly Atkinson

23. Jan 21, 2008

### Marco_84

Its getting very interesting this thread...

I just think very easly... compactified regions, curved space time... and all geometries already existed in our mind...
mathematicians, physicist and all scientist are just making possible what someBODY imagined yearsss ago.

IM SORRY FOR BEING SO CRYPTIC...

regards.
marco

24. Jan 22, 2008

### reilly

This is great topic, and fascinating and stimulating.

If you talk to neuroscientists, they will tell you that notions like free will and rationality are physiologically suspect. As one might expect, because the unconscious mind plays a much bigger role in everything we do, our conscious, rational mind, if you insist, plays a lessor role. The reasons are manifold, in the literature. As in, emotions always play a role in our moment-to-moment life.

Controversial: there is a claim for a God gene. This is based on a great deal of empirical work, mainly brain scans while the participants was doing their religious rituals -- praying, chanting, meditating and so forth.See

Amazon.com: Why God Won't Go Away: Brain Science and the Biology ...
Amazon.com: Why God Won't Go Away: Brain Science and the Biology of Belief: Books: Andrew Newberg,Eugene D'Aquili,Vince Rause by Andrew Newberg,Eugene ...

Things are never quite as clean cut as we might like to belive.

Physics: "How far can a bird fly?" Oral exam question attributed to Enrico Fermi.

Math: Discuss the properties of the semi-group of translations on the real line from 0 to infinity.

Regards,
Reilly Atkinson

25. Jan 22, 2008

### peter0302

That's awesome. I heard one that was "How many train cars can fit in the State of Illinois?"

So what's the right answer? If the bird can stop to eat and sleep he can go pretty far...