Do we really need all this funky notation?

[dimensionless]

Whenever I look at quantum physics problems I get the impression it has a lot more to do with learning some specialized notation than it does with actual physics. Don't chemists have to know this same material? There is nothing in my chemistry book that looks remotely like this.

 

[Gokul43201]

There's actually a genius to the notation itself! And who says there's no notation in Chemistry?

Chemistry is all notation. A very simple chemical equation is nothing but shorthand notation for many pages worth of quantum mechanical calculations!

 

[dimensionless]

Yes, but that simple chemical equation has some physical meaning in reality. In contrast, a typical quantum mechanical problem might say some such as this:

Consider a large number of measurements of an observable performed on the system. Show that the mean value of an observable expresses the average of the results. Assume that the spectrum of the operator consists of both a discrete and a continuous part, but for simplicity assume it to be nondegenerate.

This question does not directly refer to reality. What is the system referred to in the problem? What are the observables and how do we obtain them? I see question after question like this everywhere in quantum mechanics.

 

[vanesch]

Yes, but that simple chemical equation has some physical meaning in reality. In contrast, a typical quantum mechanical problem might say some such as this:

This question does not directly refer to reality. What is the system referred to in the problem? What are the observables and how do we obtain them? I see question after question like this everywhere in quantum mechanics.

It's just a matter of mathematical sophistication. In fact I concur with you that it is a bad idea to jump too soon to too abstract mathematics before some physical insight is develloped.
In the words of Sakurai:
"we see a number of sophisticated, yet uneducated, theoreticians who are conversant in the LSZ formalism of Heisenberg field operators, but who do not know why an excited atom radiates, or are ignorant of the quantum theoretic derivation of Rayleigh's law that accounts for the blueness of the ski".
He said that in the 60-ies, and things didn't improve on that side

You could just as well make chemistry equations very sophisticatedly sounding, by reformulating the usual wordings in terms of graph theoretical concepts ; although I'm not sure any chemist has ever pushed sophistication that far.

There's nothing wrong with mathematical sophistication, but one shouldn't run before being able to walk, and this seems to be what happens when talking about this operator stuff.

 

[Meir Achuz]

"What are the observables"
The observables are what are observable.
That is English, not QM.

 

[TriTertButoxy]

...such as the total linear momentum, the energy, or the angular momentum of the system. Stuff like that.

 

[ohwilleke]

or are ignorant of the quantum theoretic derivation of Rayleigh's law that accounts for the blueness of the ski".

Orange skis are easier to find if you wipe out on the way down.



I do share some of the frustration with the notation myself, though. For example, why so many Greek symbols when plain old Roman lettering works just fine for everyone else?

 

[ZapperZ]

Whenever I look at quantum physics problems I get the impression it has a lot more to do with learning some specialized notation than it does with actual physics. Don't chemists have to know this same material? There is nothing in my chemistry book that looks remotely like this.

You are forgetting that these are mathematical notation in most cases. These are the TOOLS!

You are also forgetting that someone could also say that all of language is nothing more than letters and symbols. How accurate do you think that would be?

The mathematics used to express physics is extremely accurate in terms of expressing the IDEA. Using words are never as accurate. Try it. Tell me in words how the electric field of an infinite line charge varies as a function of distance from the line charge. I can bet you that expressing it in mathematical form is a lot more compact and accurate.

Many people do not complain when one is required to learn musical notations when studying music. People also do not confuse those notations as being the music itself but rather a representation of the sound. So why can't people also see the same thing with mathematical representation? Most physicists and enginners read mathematical experessions almost the same way musicians read musical notes. We don't just look at the symbols, but rather what is represents. The major difference between these mathematical symbols and musical symbols is that mathematical expressions can be logically manipulated and operated on that can still reflected physical ideas.

So yes, we DO need those "funky" notations, the same way you need a larger range of vocabulary to accurately and clearly express your ideas.

Zz.

 

[leright]

I agree with zapperz.

And chemistry is a higher layer of abstraction than physics. In order for chemists to do useful things with physics, they must simplify the notation and models used. This comes at a cost of accuracy and detail, however.

Consider a simple circuit analysis problem. The problem can be solved using maxwell's equations or it can be solved using ohms law and kirchhoffs laws. Obviously ohms law is simpler and more practical than Maxwell's equations. However, these drastic simplifications come at the expense of detail and accuracy. Simplified models, which translates into simplified notation, means greater practicality but the accuracy of the models decreases. What model you use (or what level of abstraction) depends on what you are doing at the moment.

Often, to see the big picture and to do useful things simplified models are necessary, but the more complicated models and notation are still necessary.

 

[Locrian]

This question does not directly refer to reality.

It doesn't? Well, it at least has a physical meaning. Your reality might be different than mine ;)

 

[dimensionless]

You are forgetting that these are mathematical notation in most cases. These are the TOOLS!

You are also forgetting that someone could also say that all of language is nothing more than letters and symbols. How accurate do you think that would be?

The mathematics used to express physics is extremely accurate in terms of expressing the IDEA. Using words are never as accurate. Try it. Tell me in words how the electric field of an infinite line charge varies as a function of distance from the line charge. I can bet you that expressing it in mathematical form is a lot more compact and accurate.

Many people do not complain when one is required to learn musical notations when studying music. People also do not confuse those notations as being the music itself but rather a representation of the sound. So why can't people also see the same thing with mathematical representation? Most physicists and enginners read mathematical experessions almost the same way musicians read musical notes. We don't just look at the symbols, but rather what is represents. The major difference between these mathematical symbols and musical symbols is that mathematical expressions can be logically manipulated and operated on that can still reflected physical ideas.

So yes, we DO need those "funky" notations, the same way you need a larger range of vocabulary to accurately and clearly express your ideas.

Zz.

I think sign language would be a lot easier to learn than French. Also German would be easier to learn than English because German doesn't have silent letters.

I'm not arguing against mathematics. I'm just saying that there might be better ways to describe all this stuff. Maybe vanesch said it best:

it is a bad idea to jump too soon to too abstract mathematics before some physical insight is developed.

Hmmmm..musical notation? The whole system of musical notation is arbitrary and completely lacks physical meaning. I would cite Paul McCartney and Jimi Hendrix as evidence of this. Both were spectacular instrumentalist, but neither one could read musical notation.

Some things are more complicated than they need to be. Once languages, such as English, became standardized they became unnecessarily complex. Why can't I starts a sentence with a preposition? Why must I use the letter "w" to spell the word "write?"

 

[ZapperZ]

I think sign language would be a lot easier to learn than French. Also German would be easier to learn than English because German doesn't have silent letters.

I'm not arguing against mathematics. I'm just saying that there might be better ways to describe all this stuff.

Show me one.

Zz.

 

[masudr]

Some things are more complicated than they need to be. Once languages, such as English, became standardized they became unnecessarily complex. Why can't I starts a sentence with a preposition? Why must I use the letter "w" to spell the word "write?"

Most (if not all) mathematical language rarely have redundancies of the type you are describing. In fact, that's why physicists tend to rely on mathematics as it is a precise language.

 

[eljose]

-Most problems with Notation come from Latin..in fact in the XVII-th century Newton and others wrote in Latin, so it was normal for them to write the Latin words "momentum"...or "Infinitum"..which sometimes can be confusing.

-Although in my opinion is more stupid..the "Name notation"..for example if Lagrange studied a function we call it "Lagrangian"..if Euler studied some Integral we call it "Eulerian"..this sometimes makes me feel stupid, as a example the "Abel-Plana" formula (Plana=flat in Spanish) or "Perron formula" (Perron sounds similar to "big dog" in Spanish) or the unpronounciable word "stieltjes" (german mathematician related to a kind of integral) at least in Spanish..or the "funny" anecdote of "rodrigues formula"..many of the people studying physics in Spain believe he was a Mexican man instead of being French.

 

[Timbuqtu]

... "stieltjes" (german mathematician related to a kind of integral) ...

He was Dutch

 

[Quaoar]

I do think that quantum mechanics is beautiful, however I think all undergraduate texts do an awful job of introducing the notation. The biggest problem I find with these books is that they'll explain a certain nuance once, and in all future manipulations/derivations, the intermediate steps are all ignored. I know I shouldn't need to have my hand held, but considering how radically different the notation is from the mathematics used in other physics disciplines, they really should be as detailed as possible.

Basically, I buy a book to learn how something works. I don't like books that force me to derive something from first-principles every single time (Gasioworitz is the WORST offender in this regard). I think this problem isn't encountered in other undergraduate physics texts, at least not to such a severe degree.