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Which one is the Planck's constant?

  1. Apr 26, 2005 #1
    I have a minute problem here. Some of the QM books have treated [itex]h[/itex] as the Planck's constant while some [itex]\hbar[/itex] as the Planck's constant. So can someone resolve this difficulty for me? Thanks in advance!
     
  2. jcsd
  3. Apr 26, 2005 #2
    h-bar is 'Reduced Planck's Constant' or 'Dirac's Constant' (h/2pi).

    Jono
     
  4. Apr 26, 2005 #3

    James R

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    Both are often referred to as "Planck's constant". There's really no confusion, since two different symbols are used.

    [tex]\hbar \equiv h / 2\pi[/tex]
     
  5. Apr 26, 2005 #4

    dextercioby

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    Planck's constant is [itex] h [/itex] and Dirac's constant is [itex] \hbar[/itex].The Bohr model of the atom is responsable for the "reduction" by [itex] 2\pi [/itex] (because the orbits were circular).

    Daniel.
     
  6. Apr 26, 2005 #5

    selfAdjoint

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    And also because the wave function is of the form [tex]e^{i\phi}[/tex] which defines the unit circle in the complex plane.
     
  7. Apr 26, 2005 #6

    dextercioby

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    He asked about the origin of [itex] \hbar [/itex].I told him where it first appeared.Not the notation (that is due to Dirac,hence the name),but that [itex]2\pi [/itex].

    In the context of quantum mechanics,it appears for the first time in Born & Jordan [1] commutation relations...

    Daniel.

    -----------------------------------------------------------
    [1]M.Born,P.Jordan,Zeits.f.Physik,34,858 (1925).
     
  8. Apr 26, 2005 #7
    May I ask. What is the purpose of Planks Constant [tex]p[/tex]anyway? :woundering:
     
  9. Apr 26, 2005 #8

    dextercioby

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    Proportionality constant between the energy of a quanta of radiation & the radiation frequency...?It has dimensions of action/angular momentum which is very important throughout any quantum theory.

    Daniel.
     
  10. Apr 27, 2005 #9
    He? It is her! Anyway, thank you for the clarification. I realized that the older QM books have treated [tex]h[/tex] as Planck's constant while the latter versions have it as [tex]\hbar[/tex].
     
  11. Apr 27, 2005 #10

    dextercioby

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    I'm sorry,but i think 'latter' versions use the word "reduced" when speaking of "eitchbar".

    Daniel.
     
  12. Apr 27, 2005 #11
    Gasiorowicz's book on "Modern Physics" has not used the word "reduced" in particular. Anyway he was referring to same thing you mentioned I guess :wink:

    Here is an excerpt:

     
  13. Apr 27, 2005 #12

    dextercioby

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    I agree that not too many people use the syntagma 'Dirac's constant' when speaking about 'hbar'.But that doesn't justify in any way mixing up hystorical events...

    Daniel.
     
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