Which one is the Planck's constant?

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Discussion Overview

The discussion revolves around the identification and usage of Planck's constant, specifically the symbols \( h \) and \( \hbar \). Participants explore the historical context, definitions, and implications of these constants within quantum mechanics.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Historical

Main Points Raised

  • Some participants note that both \( h \) and \( \hbar \) are often referred to as "Planck's constant," with \( \hbar \) defined as \( h / 2\pi \).
  • One participant explains that the term "Dirac's constant" is sometimes used for \( \hbar \), but emphasizes that \( h \) is the original Planck's constant.
  • Another participant discusses the historical significance of the factor of \( 2\pi \) in the context of the Bohr model and its relation to circular orbits.
  • There is mention of the first appearance of \( \hbar \) in the context of quantum mechanics, specifically in the work of Born and Jordan regarding commutation relations.
  • One participant expresses confusion about the terminology used in different quantum mechanics texts, noting that older books typically refer to \( h \) as Planck's constant while newer texts may refer to \( \hbar \) as the reduced Planck's constant.
  • Another participant asserts that newer texts often use the term "reduced" when referring to \( \hbar \), while also referencing a specific textbook that does not use this terminology.
  • There is a correction regarding the gender of a participant in the discussion, indicating a personal engagement in the conversation.

Areas of Agreement / Disagreement

Participants express differing views on the terminology and historical context surrounding \( h \) and \( \hbar \). There is no consensus on a single interpretation, as various perspectives on the usage and naming conventions persist.

Contextual Notes

Some statements reflect historical interpretations and the evolution of terminology in quantum mechanics literature, which may vary across different texts and authors.

Reshma
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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!
 
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h-bar is 'Reduced Planck's Constant' or 'Dirac's Constant' (h/2pi).

Jono
 
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]
 
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.
 
dextercioby said:
The Bohr model of the atom is responsable for the "reduction" by [itex]2\pi[/itex] (because the orbits were circular).

Daniel.

And also because the wave function is of the form [tex]e^{i\phi}[/tex] which defines the unit circle in the complex plane.
 
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).
 
May I ask. What is the purpose of Planks Constant [tex]p[/tex]anyway? :woundering:
 
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.
 
dextercioby said:
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).

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].
 
  • #10
I'm sorry,but i think 'latter' versions use the word "reduced" when speaking of "eitchbar".

Daniel.
 
  • #11
dextercioby said:
I'm sorry,but i think 'latter' versions use the word "reduced" when speaking of "eitchbar".

Daniel.

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:

In older literature, the name Planck's constant was reserved for [tex]h[/tex], the quantity mentioned in the historical introduction, without division by [tex]2\pi[/tex]. Now h-bar is commonly treated a Planck's constant.
 
  • #12
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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