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Thread: Why is Planck's Constant routinely divided by 2•pi?

  1. #1 Why is Planck's Constant routinely divided by 2•pi? 
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    Quote Originally Posted by Catherton318
    Why is Planck's Constant routinely divided by 2•pi?
    First off, welcome to the forum!

    Because the expression appears to often in quantum mechanics, more than h does separately. In fact that's why they introduced a new symbol for it, i.e. .
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    Yes I'm referring to Dirac's Constant.

    I'm wondering for what purpose Planck's Constant is divided by 2•pi, and why specifically 2•pi?

    Thanks for the welcome!
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    Quote Originally Posted by Catherton318 View Post
    Yes I'm referring to Dirac's Constant.

    I'm wondering for what purpose Planck's Constant is divided by 2•pi, and why specifically 2•pi?

    Thanks for the welcome!
    Physicist noted that 2pi recurs with sufficient frequency (bad pun intended) that this factor is frequently absorbed into "h-bar." What he didn't say was why 2pi recurs so frequently, which I guess is your real question. The answer is that conversions between "ordinary" frequency (cycles per second, or Hz) and radians per second, show up all the time. The relationship between these two frequency measures involves the 2pi factor (the number of radians per cycle). I suppose we could've absorbed the term somewhere else, but if we had, someone would be asking your question about why we chose that term.
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    It facilitates a change in geometry?
    .
    Electrons are said to exist in a "cloud" and are "spread out". When an atom ionizes it loses an electron yet still manages to stay intact, waiting around for another electron to localize. But "photons" have no mass, and are not localized. A photon exists in a wavefunction, its energy being evenly distributed throughout its wavelength. Light does not slow down as it bounces back and forth between mirrors, meaning it does not exert any pressure on those surfaces, meaning it in fact has no mass.

    It seems to me like light (or the "photon") is pure energy and upon localizing becomes an electron? It's a change in geometry, between 1 and 2 dimensions that is important.

    Does any of that make sense? I'm an amateur, mind you.
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    Quote Originally Posted by Catherton318 View Post
    It facilitates a change in geometry?
    Not quite. It's more of facilitating translations between two equivalent measures of a geometric property.

    Electrons are said to exist in a "cloud" and...
    The geometric property in question has nothing specifically to do with electrons, clouds, wavefunctions or the like.

    One can express frequency in a number of equivalent ways. In this case, we're talking about the number of cycles per second, or the number of radians of phase elapsed each second. The relationship between these two measures involves the 2pi factor.

    So where's the connection with QM? The energy of a photon is related to frequency. Whether you express frequency in radians per second or Hz determines whether or not 2pi makes an appearance. And if you wish to make it disappear, you may employ h-bar.
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    Right, the energy of a photon IS its frequency, in essence, since light has no mass.

    Incidentally, I'm confused why a photon is said to have inertia? Light will speed up instantly and automatically when leaving glass, so how can it have inertia? And if it does not have inertia, how is it thought that light (a "photon") is able to eject electrons from their atomic locations?
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    Quote Originally Posted by Catherton318 View Post
    Right, the energy of a photon IS its frequency, in essence, since light has no mass.

    Incidentally, I'm confused why a photon is said to have inertia?
    I would be confused, too, because that's not a mainstream understanding. Photons have momentum, which is not the same thing.

    And if it does not have inertia, how is it thought that light (a "photon") is able to eject electrons from their atomic locations?
    Photons have energy and momenta. Interactions, including ejection of electrons, will satisfy the associated conservation laws.
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    You could also look at the relationship between the Compton wavelength and the reduced Compton wavelength.

    Compton wavelength - Wikipedia, the free encyclopedia

    Relationship between the reduced and non-reduced Compton wavelength

    The reduced Compton wavelength is a natural representation for mass on the quantum scale. Equations that pertain to mass in the form of mass, like Klein-Gordon and Schrödinger's, use the reduced Compton wavelength. The non-reduced Compton wavelength is a natural representation for mass that has been converted into energy. Equations that pertain to the conversion of mass into energy, or to the wavelengths of photons interacting with mass, use the non-reduced Compton wavelength.

    A particle of rest mass m has a rest energy of E = mc^2. The non-reduced Compton wavelength for this particle is the wavelength of a photon of the same energy.
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    Quote Originally Posted by Catherton318
    Right, the energy of a photon IS its frequency, in essence, since light has no mass.
    The energy of a photon is proportional to its frequency, not "is" it's frequency. Frequency and energy are very different things. Being proportion to something is not the same as being that thing.

    Quote Originally Posted by Catherton318
    Incidentally, I'm confused why a photon is said to have inertia?
    Because it has mass. When you said that a photon has mass above what that means is that it has zero proper mass. People often confuse that with having zero inertial mass. However photons do have inertial mass which is sometimes referred to as relativistic mass. See

    Relativistic mass
    What is the mass of a photon?

    Quote Originally Posted by Catherton318
    Light will speed up instantly and automatically when leaving glass, so how can it have inertia? And if it does not have inertia, how is it thought that light (a "photon") is able to eject electrons from their atomic locations?
    In special relativity it is best to think of inertia as that property which gives a particle it's momentum, not which makes it difficult for the particle to change its velocity.

    It you want to read more about this then I recommend downloading the following texts

    Relativity: Special, General and Cosmological, Rindler, Oxford Univ., Press, (2001), page 120
    From Introducing Einstein's Relativity, Ray D'Inverno, Oxford Univ. Press, (1992), page 50
    Special Relativity, A. P. French, MIT Press, page 20

    from Electronic library. Download books free. Finding books
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    Quote Originally Posted by Physicist View Post


    Because it has mass. When you said that a photon has mass above what that means is that it has zero proper mass. People often confuse that with having zero inertial mass. However photons do have inertial mass which is sometimes referred to as relativistic mass. See

    Relativistic mass
    What is the mass of a photon?

    The notion of "relativistic mass" is obsolete in contemporary physics. As such, it makes no sense to claim that "photons do have inertial mass which is sometimes referred to as relativistic mass". Photons are massless particles and this is all there is to it.
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