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Tackling the middle ground of quantum mechanics

  1. Nov 8, 2012 #1
    I have made a focused effort over the past couple years to understand this "miracle" of quantum mechanics that has changed the civilization we live in, and frankly, I'm getting a bit frustrated that I am not privy to, as most popular TV physicists seem to purport, the obviousness of the translation of its mathematics to the wonders of modern technology.

    What I mean is that I'm not doubting it, I use the technology that quantum theory has putatively produced everyday just like everyone else. However, I am having trouble understanding how solving the SE equation for a "particle in a box," or an "infinite square well," or the “energy states of the hydrogen atom,” or the “probability of finding a particle in a certain location,” translate to this wonderful world of color TV, cell phones, time travel, black holes and quantum teleportation.

    Maybe its obvious to everyone else, but not me. All I get to enjoy is complex conjugates, second derivatives, Dirac notation, phasors, Hamiltonians, and a bevy of other mathematical and notational jungles. Which I’m happy to navigate, but I’d like some kind of a middle ground understanding of how knowing the probability of finding a particle in a certain location “in a box” or even in some arbitrary spatial context is useful. Yeah, I know about the energy levels and the energy bands in their relation to semiconductors, but what about the rest? Why is everything I read and study on the subject so myopic in its scope of a greater practical relevance? It is getting very discouraging. Any comments and/or links would be appreciated.
  2. jcsd
  3. Nov 8, 2012 #2
    Ok, perhaps I should state my quandry more colloquially--it is very easy to see the everyday relevance of studying, say newtonian mechanics f=ma, in order to predict the ballistic trajectory of a cannonball, the motion of a double pendulum, or a mass sliding down an incline plane. Its even easy to see the practical relevance of relativity theory in regards to GPS and relativistic time dilation and mass increase of the accelerated protons at the LHC.

    What I am NOT finding, however, is any sort of similar connection to my everyday experience, or even some abstract sense of relevancy, of this overwhelming preoccupation of quantum physicists to understand the probability of finding a particle in some arbitrary location. Does that make any sense to anyone?
  4. Nov 9, 2012 #3
    There is tremendous amount of examples that can be given...

    Consider the electrons in an atom. Their probability distribution is needed to be known if we would like to predict how the atoms interact with each other in order to form molecules. The molecular orbitals are also useful if we would like to know the chemical properties of a molecule. These information and many more relevant, are needed in order to build chemistry and then use it in industrial, pharmaceutical, etc. applications, that you encounter in everyday life.

    I think that the problem in your understanding lies in the fact that QM results are not linked directly to everyday-life phenomena, but they have to be processed in various levels on order to be connected with the phenomena. Maybe it will help you to see things in the opposite way: instead of asking “how that QM thing is connected to my experience” you should ask “how can I understand that thing from my everyday life, in the most fundamental level”. Doing this, you will have to pass through various levels of understanding and in each level ask various kind of questions, witch in they turn are answered by a deeper level of understanding. Eventually, you will reach a level that the questions you make are the ultimate ones, in the sense that after they answered, no other question can be made that can be answered by human knowledge. Well, that level will lie just above QM (or theoretical physics in general).
  5. Nov 9, 2012 #4


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    I think you have answered your own question with the reference to GPS. These work by using general relativistic equations. Yet there was no obvious practical benefit for those equations for years after they were derived other than for cosmological purposes.

    Much of the advanced work in quantum mechanics has no immediate obvious impact. Yet we could still be just one application away from something really important for the future. Much of the benefit from QM has been in applications that appear today to be more like blocking and tackling. But that is simply a matter of perspective, you could just as easily look at those as miraculous. So where you sit matters. I.e. if you aren't working with cannonballs, then F=ma is pure theory too.
  6. Nov 9, 2012 #5
    Some examples that might illustrate how important Quantum mechanics is in everyday-world. Try to answer the folowing questions:
    - Why are different elements chemically so different? (Explanation requires energy levels and Pauli exclusion principle)
    - Why do I get a sun-burn from UV light, but not from visible light (requires knowledge of photon as energy packets and energy levels in the molecules that get afected by them)
    - Why do I not fall through the floor? (requires electron shells and the Pauli exclusion principle)
    - Why do metals conduct heat so well but don't have a huge heat capacity (requires the Sommerfeld model of the electron gas).

    The list could be extended endlessly...

    Or is your question more concerned only with the Born interpretation of the wave function? There, it is indeed a bit more tricky to find good examples in the everyday world - that is simply due to statistics.
    I'll try an analogy to explain why we don't see those effects so often: Each person is a hugely complex being and their decisions are almost impossible to predict. However, it is much easier to predict the decisions of a statistical sample of people.
    Still, there are some cool examples of strange quantum effects - the magnetic compass of some birds for example is probaby due to a quantum entanglement of molecular excitation states.
  7. Nov 9, 2012 #6
    Thanks Dust. I guess my concern is more didactic in nature. It's been a long hard slog learning how to understand this quantum mechanics thing the right way, with all the advanced mathematics and conceptual absurdity you are supposed to "swallow" along the way. And, after all that, it seems as though all you're rewarded with at the end of the day is some ambiguous notion of some abstract probability you will find an electron in some corner of a box.

    The situation is different in classical physics and relativity. If you have a good instructor, they will tend to incorporate the mathematical physics you are being taught into practical examples so that every once in a while you get the "gee wiz" effect whereby you can see how your efforts give you deeper insight into the world you live in. It is these gee wiz moments that inspire one, at least me, to continue doing the hard work.

    So, my general frustration is that I've spent a lot of time trying to find that resourse, whether it be written text or videocourse, that reminds you from time to time how what you are learning relates to SPECIFIC pratical applications. In my expereince, every instructional resource I have found has left me not with the inspiration to continue my pursuit of quantum mechanics, but rather has left me wondering how I am going to escape from this infinite well of drudgery, confusion, and seeming pointlessness.

    If anyone knows of a good resourse I have missed, please let me know.
  8. Nov 9, 2012 #7
    I wrote my previous reply while Dr Chinese and Sonderval were writing theirs so it may seem something of a nonsequitor. In any case, thanks to all for your comments. All is well noted, I am very exited about the subject. It just puzzles me sometimes why some people, especially this large slew of academic youtube videographers, spend a considerable amount of time and effort on these putatively instructional videos on quantum wave functions, etc., and then never take that discussion "outside the box," so to speak. Why take the time to parrot the exact same stale presentation of the particle in the box problem and give absolutely zero additional insight into the issue as anyone else?

    I study and teach in the field of cognitive neuroscience, and try very hard to point out the larger, practical relevance of what I am discussing. I am just not finding that it in my QM studies, unfortunately.
  9. Nov 9, 2012 #8


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    1. The largest application of QM is in solid state physics. All of the electronic devices you use rely on semiconductors, and semiconductor physics is all quantum mechanical. Indeed, even conduction in a metal wire, and why some materials conduct and others insulate, could not be fully understood before QM developed the concept of electron energies and bands. As transistor and IC features have shrunk to nm size, QM effects have moved from important to dominant.

    2. Second largest area is chemistry. The periodic table was a mystery before the Pauli exclusion principle, and energy levels and shells. No one could understand chemical bonding--hybridization, bond angles, etc.--at all.

    3. Nanoparticles and nanomachines require QM to understand them because of their tiny sizes. Strange scaling is often observed. In our world magnetics is used for motion (motors)m but nanomotors are electrostatic, instead. Friction is another thing that behaves strangely at the nano scale.

    4. Biological investigations are increasingly quantum mechanical as we move to smaller scales. For instance, protein conformation (folding and shape), which makes the bio world go round--immunology, replication, etc.--involves chemistry, bonding, and physics at the nm scale.

    5. Nuclear magnetic resonance is a quantum phenomenon, and its use in protein chemistry involves heavy use of QM. Even NMR measurement techniques bear the quantum name (like "double quantum filtering"). NMR's use in magnetic resonance imaging is widespread and well-known.
  10. Nov 9, 2012 #9
    I think you just encountered one of the problems we often see in teaching physics: Trying to teach the (important and difficult) mathematics, people forget in the end to actually interpret the equations and tell what they actually mean - how often do we all see a complicated derivation of several pages that ends with some final equation that is then not really looked at.
  11. Nov 9, 2012 #10
    Lasers, masers, anything to do with superconductivity. These all rely directly on quantum effects for their behaviour.

    The thing you have to remember is the particle-in-a-box is just the very beginning of quantum mechanics. When you generalize it to lots of particles in the potential from lots of nuclei arranged in a crystal, then you start to do solid state physics.

    When you start to apply the principle of the simple harmonic oscillator (another particle in a potential), to a whole mode of oscillation of a classical field, then you begin to do quantum field theory.

    Quantum mechanics 101 seems a bit remote from applications, I agree. But it really does start to get exciting with quantum mechanics 102, 103....

    Then when you get to quantum mechanics 201, you start to realize how fascinatingly weird the stuff in quantum mechanics 101 really was, and you start to appreciate it.
  12. Nov 9, 2012 #11
    Ok, great stuff, I guess I'm just suffering growing pains tryin to cut my teath on this stuff. And what you are telling me that it is a coarse grain, but, in the end the payoff will be there. That is an optimistic optimism and I like it. Kind of like a second derivative. What I take from this is that you have to continue to do the hard math and persevere and then at some point a bifuration will appear whereby you break through the other side. I like that consciousness. And I hope to soon inform this cool community if and when it does.
  13. Nov 10, 2012 #12
    As has been pointed out, perhaps your most frequent every-day level encounter with quantum mechanics is when you use a USB flash drive. The functionality of those devices depend entirely on the electrons tunneling out of their atomic bound states.
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