Which one is the Planck's constant?

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In summary: Here is an excerpt:"Now h-bar is commonly treated as a Planck's constant.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...,"
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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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  • #2
h-bar is 'Reduced Planck's Constant' or 'Dirac's Constant' (h/2pi).

Jono
 
  • #3
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]
 
  • #4
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.
 
  • #5
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.
 
  • #6
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).
 
  • #7
May I ask. What is the purpose of Planks Constant [tex]p[/tex]anyway? :woundering:
 
  • #8
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.
 
  • #9
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.
 

1. What is Planck's constant and why is it important?

Planck's constant, represented by the symbol h, is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. It is important because it helps us understand the behavior of particles on a microscopic scale and is the basis for many important equations in physics.

2. How was Planck's constant discovered?

Planck's constant was first discovered by German physicist Max Planck in 1900. He was trying to explain the behavior of blackbody radiation and found that the energy of the radiation was directly proportional to its frequency, with the constant of proportionality being Planck's constant.

3. What is the value of Planck's constant?

The value of Planck's constant is approximately 6.626 x 10^-34 joule-seconds (J·s). This value is a constant and does not change, regardless of the specific context in which it is used.

4. How is Planck's constant used in everyday life?

While Planck's constant may not have an obvious impact on our daily lives, it is used in many modern technologies, such as LED lights, solar cells, and computer chips. It also plays a crucial role in understanding the behavior of atoms and molecules.

5. Is there an easy way to remember the value of Planck's constant?

One way to remember the value of Planck's constant is to associate it with the number of letters in the word "Planck." Another way is to remember the digits 6-2-6-6, which correspond to the first four digits after the decimal point in the value of Planck's constant.

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