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Quantum mechanics or quantum theory?

  1. Oct 8, 2011 #1
    Hi all,

    Can someone please explain to me how/when to properly use the terms quantum mechanics, quantum theory, and quantum physics? They aren't exactly interchangeable are they?

    Thanks,
     
  2. jcsd
  3. Oct 8, 2011 #2

    dx

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    They are used interchangably by most people.
     
  4. Oct 8, 2011 #3

    Ken G

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    Actually, I think it's important to stress that the "theory" is just one-- there is only one machine there for making predictions, and it is not in chaos, it is probably the best theory physics has ever developed. Interpretations of the theory are where the chaos comes in, but fortunately for science, the theory works the same in any interpretation.

    I agree that "quantum mechanics" and "quantum theory" seem pretty interchangeable terms. If I were to draw a distinction, I would point to the usual experiment/theory synergy in science, and say that the term "quantum theory" seems to intentionally leave out experiments, whereas "quantum mechanics" seems more inclusive of the experimental outcomes. A course on "quantum mechanics", for example, might actually begin with the observations, and move to the theory later, whereas we might not be surprised if a course on "quantum theory" dives right into the mathematical postulates of the theory on day one, and refers to observations later on and only to motivate why we have confidence in the theory.
     
  5. Oct 8, 2011 #4
    Okay, what about "Quantum Chemistry"? That's what my textbook's title is called.
     
  6. Oct 9, 2011 #5

    Ken G

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    It's pretty standard practice though. For example, consider classical mechanics-- is this a theory about forces, a la Newton, or a theory about energy, a la Hamilton? Are the laws causal (forces cause acceleration), or are they extremum principles (what happens is what minimizes action)? These are completely different interpretations, yet present no controversy-- everyone is pretty happy with the idea that classical mechanics works the same when presented from either perspective.

    So why do we view there as being such "chaos" in quantum theory? I think it is simply because we always tend to care more about interpretations of our current best theory-- old theories that are known to break down in certain situations are treated much less seriously. If we simply treated our current best theories with the same grain of salt we use for old theories, the problem goes away immediately.
    Actually, virtual particles make an excellent example of why interpretations are not that important. The theory does not propose them-- they are a kind of pictorial way of understanding a certain approach to solving the equations of the theory. But the equations are the theory, not the way of solving them. So some take virtual particles seriously as part of our picture of what is actually happening, others see them as purely a way of talking about a solution technique, with no intrinsic physical meaning whatsoever. Yet both camps do the same calculations and get the same answers, so there is just no real problem there.
     
  7. Oct 9, 2011 #6

    Ken G

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    I would say that chemistry is generally interested in somewhat less fundamental kinds of interactions. Often, chemistry is interested in how groups of molecules interact with each other, rather than the more fundamental pieces of those interactions. So physics tends to be highly reductionist, like if you could understand what is happening in the head of a pin you could understand the universe. Chemists don't care about heads of pins, they care about what happens when certain chemicals mix, and as such they are often closer to chemical engineering than physics is to, say, mechanical engineering. Still, chemists would often say they are interested in basic science about chemical reactions, moreso than particular applications.

    These are just generalizations, of course, but I would say that "quantum chemistry" is the chemistry that you must understand quantum physics to understand, but the stress would not be on the quantum physics per se, but rather how the quantum physics is affecting how the collection of molecules interact. It is not terribly uncommon for quantum physics classes to never mention molecules at all, whereas quantum chemistry will focus much of the attention there.
     
  8. Oct 9, 2011 #7

    Fredrik

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    That's how I would describe the difference between "quantum theory" and "quantum physics". "Quantum mechanics" doesn't sound like something that includes experiments to me.

    I would say that we need one name for the theory of wavefunctions, the Schrödinger equation, etc. that we all encounter in the first course we take with "quantum" in the title, and another name for the larger framework that contains all quantum theories. (That stuff about wavefunctions is really just the quantum theory of a single particle with interactions with the outside world that can be represented by a "potential"). I use the term "wave mechanics" for the stuff about wavefunctions, and "quantum mechanics" for the larger framework. (This is consistent with how "classical mechanics" is a framework in which you can define many more specific theories by specifying a number or particles and/or fields, and their interactions). I consider "quantum theory" to be interchangeable with "quantum mechanics". However, there are are people who use the term "quantum mechanics" for that specific theory of a single particle and a potential. I guess they would need a name for the larger framework, and "quantum theory" would be an excellent choice.
     
  9. Oct 9, 2011 #8

    Ken G

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    Yes, I could see using "quantum physics" to include the observations, and then quantum mechanics would just be synonymous to quantum theory.
    The trouble there is that "wave mechanics" is already used for applications involving the classical wave equation, not the quantum Schroedinger equation. It's true that we now know the latter subsumes the former, but all the same, there remains the field "wave mechanics" that is unquantized and deals simply with propagating real functions of the form f(x-vt). But I see your point that single-particle wavefunctions are the ones that are like "waves", so that connection should be emphasized in the terminology. Perhaps "wavefunction mechanics"?
     
  10. Oct 9, 2011 #9

    alxm

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    That's not what quantum chemistry is at all. Seriously, if you don't know what the field is, don't make up a guess.

    There exists no distinct area of chemistry that requires understanding quantum mechanics to understand. It all requires quantum mechanics to understand. Without QM, there would be no theories of chemical reactivity or bonding and so on, period. Concepts like the Pauli principle, electron spin, orbitals and wave functions are all part of first-year undergrad-level chemistry these days, and have been since the 1940's. Every qualitative and conceptual model used in chemistry, by every chemist, is rigorously based on quantum mechanics.

    Quantum chemistry is the explicit quantum-mechanical study of atomic and molecular systems. As opposed to the implicit and qualitative use of it in the simplified models. It borders on theoretical physics and chemistry, physical chemistry, chemical physics, atomic/molecular physics, and solid-state physics. And it's just as much a branch of physics as solid-state is (which, seen in a broader context, involves the exact same physical interactions, treated under a different set of boundary conditions). There is indeed a "stress on the quantum mechanics per se", because you can't possibly learn applied quantum mechanics without a solid understanding of actual quantum mechanics. Quantum chemistry's use of QM involves both non-relativistic and relativistic (Dirac equation) QM, although not so much QFT, as QED effects are generally negligible in in most situations studied there.

    Quantum chemistry primarily involves solving the molecular Schrödinger (or Dirac, or Kohn-Sham) equation to quantitatively calculate chemical properties, and developing the physical approximations and mathematical methods necessary to do so. In which area it overlaps also with the method-development parts of Solid State but also Nuclear physics, which also deal with the quantum many-body problem. E.g. DFT originated as a solid-state method, later applied to QC. Coupled-cluster originated as a nuclear physics method. The Hartree-Fock method developed in QC became the HF-Bogoliubov method in nuclear physics. Et cetera.

    In the term "quantum chemistry", "chemistry" denotes what's being studied and "quantum" denotes the methodology - the fact that it involves explicit quantum-mechanical calculations of the electronic structure. (and possibly quantum mechanical actions of the nuclei) It does not mean that it deals with things that are any more or any less quantum mechanical than what the rest of chemistry deals with.

    Quantum chemistry is not simplified quantum-mechanics-for-chemists. That much (in the form of Valence Bond theory and Molecular Orbital theory, etc) is already taught in introductory General Chemistry. It is the branch of applied physics and theoretical chemistry that involves explicit quantum-mechanical calculations and the related methodology, for the chemical properties of molecular systems. As opposed (for instance) to theoretical solid-state, which is the same applied to solids, or theoretical atomic/molecular physics, which focuses more on spectroscopy and exotic states of matter that don't traditionally fall in the realm of 'chemistry'.

    Most quantum physics courses don't focus on molecules, but they don't focus much on the in-depth details of anything that has a whole field devoted to it.
     
  11. Oct 9, 2011 #10

    Ken G

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    I think you missed that I stressed the differences. Clearly quantum chemistry is a whole lot like quantum physics, which is what you seem to be stressing. I think the questioner wants distinctions.
    That's not a very realistic position. You might as well state that all of physics requires quantum mechanics to understand, for exactly the same reasons. No physicist would ever claim that, however, as it would leave out the vast majority of what physicists actually do (which doesn't use quantum mechanics nor require daily contact with an understanding of it). I'm sure the same is true for chemists, most of whom recall quantum mechanics from the last time they taught quantum chemistry and little else-- just like most physicists.
    Yes, I didn't mean to be interpreted as saying that. By saying chemistry doesn't stress the fundamentals as much as physics does (which is true), I didn't mean to suggest chemists were less intelligent or less rigorous in what they do.
    Right, and those are not stressed in physics courses. So when physics curricula get around to quantum mechanics, there's no "now let's see how quantum mechanics explains those valence bond and molecular orbital issues", whereas chemistry does have that element, which is why I stressed molecules and chemical reactions. I didn't mean those topics aren't in themselves "fundamental" in some absolute way, they are just not fundamental from the physics perspective.
    Yes, I believe that is more or less what I said it was, but I'm glad you could clarify from a more informed perspective.
     
  12. Oct 9, 2011 #11

    alxm

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    No, you seem to miss the point entirely. Quantum chemistry is not 'like' quantum physics. It's an application of quantum physics to molecules, just as solid-state physics modelling is to crystals, and nuclear physics is to nucleons, and so forth.

    You have to study quantum physics before you can learn quantum chemistry. I'm not sure why this would be so hard to grasp. You have to study QM before you can learn the methods and math to calculate band gaps in solid-state (and that too, is a specialized application), and so for HOMO/LUMO energies in quantum chemistry. (Those two concepts are in fact the same thing, and calculated using essentially the same methods)

    If someone's got a textbook on quantum chemistry without having studied QM before (Is it Levine's book?), then it's almost certainly an introductory textbook that first contains a run-through of basic of QM before going into basic QC. But anyone wanting to specialize in QC will need to know grad-level quantum mechanics.
    No, because there's a classical theory of physics, which is applicable in some situations. There is no 'classical' theory of chemistry whatsoever. That does not mean (non-quantum) chemists know or use the formalism and math of quantum mechanics, though.
    Most chemists don't know any quantum chemistry! It's a sub-field. And most quantum chemists are actually physicists. My PhD is in physics ("chemical physics"). My old supervisor's doctorate (and his old supervisor's doctorate, in turn) was in "theoretical physics". I currently work on a physics faculty. The field is an offshoot of theoretical physics, not of chemistry, because again: There was no real theory of chemistry prior to QM. The pioneers of QC were Heitler, London, Slater, Mulliken, Pauling, Hund, Born, etc.. All physicists, mainly theoretical physicists.

    The reason why it's long been mostly physicists, is precisely because most chemistry students are a bit loath to study up on the prerequisite level of math and QM.
    I didn't think you did. But the difference here is that ordinary chemists learn conceptual, approximate models (VB/MO theory). Those are rigorously based on QM, but they don't learn the derivations or math behind it (unless they actually go into QC, which as I said, requires that you learn QM first). There's no real math with those models, because they're not quantitative. That's not considered quantum chemistry as much as standard chemical theory. It's known by every chemist, and used by most of them, with the only exception perhaps being some biochemists who are studying things that don't have to do so much with chemical bonding and reactivity.

    But quantum chemistry is not taught like chemistry. It's taught like physics. It most certainly does involve the fundamentals. In a QC textbook, everything is derived mathematically from first principles, in the same manner it is in any physics textbook where quantum theory is applied to more in-depth modelling applications. Is http://arxiv.org/abs/1108.1104" [Broken] quantum chemistry or solid-state physics? It's both, in fact. But it's not actual chemistry.
     
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  13. Oct 10, 2011 #12

    Ken G

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    I know it is an application of quantum physics to molecules, that's why I implied it was an application of quantum physics to molecules in my original answer. I presumed that the person asking the question knows why "quantum" appears in the title "quantum chemistry", so what they want to know is, how is it distinguished from "quantum physics." The answer, we appear to agree, has to do with quantum physics is aimed primarily at the fundamental level (the usual focus in physics) versus quantum chemistry is applied to molecules and chemical interactions (the usual focus in chemistry). If you think I was saying anything different from that, then I must not have expressed it very clearly.

    It's not hard to grasp at all, in fact it's perfectly obvious, but irrelevant to the question that was asked.
    I certainly agree with that. But it isn't relevant to the question of what are the differences between quantum chemistry and quantum physics. I agree with you they are only differences in focus, differences in emphasis, differences in the questions that are viewed as most important. That's just the meaning I was attempting to convey-- the emphasis of chemistry is on molecules and chemical interactions, but the emphasis of physics is even more reductionist than that.
    So what!? The question was about the differences, not the ways in which they are the same. If someone asked me about the differences between astronomy and physics, I wouldn't start by saying that many physicists do astronomy.
    Yes, there is great overlap. Hence the term "quantum" in common. But you still haven't answered the question-- what is the difference between quantum chemistry and quantum physics? Don't you think that is what Runner_1 wanted to know? I certainly didn't mean to convey the impression that quantum chemists didn't know any physics. What I said is that it is a different emphasis on the issues of interest that differentiates quantum physics and quantum chemistry, and that is still what distinguishes them. Even if most quantum chemists are trained as physicists, that is still what distinguishes them, because there are plenty of physics departments that also have people doing quantum mechanics, and it's not just a roll of the dice that determines which department people find jobs in.
    Which exposes the fundamental differences in emphasis between chemistry and physics. You're just saying that quantum chemistry is the side of chemistry that is a whole lot more like physics, and that's certainly true-- but it's still chemistry, so the question is, why is it considered chemistry and not physics? That's the question I was answering. It's just a difference between the questions "what is quantum chemistry" and "what are the differences between quantum physics and quantum chemistry". Since we'd already talked a lot about what quantum physics was, I was answering the second question, and you're starting from the ground-up and answering the first one. That doesn't make either answer wrong. If someone asked me the difference between astronomy and physics, there would be little point in citing papers on cosmology and general relativity and asking whether they are astronomy or physics-- that wasn't what the question was asking.
     
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