Which one is the Planck's constant?

[Reshma]

I have a minute problem here. Some of the QM books have treated $h$ as the Planck's constant while some $\hbar$ as the Planck's constant. So can someone resolve this difficulty for me? Thanks in advance!

 

[JonoF]

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

Jono

 

[James R]

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

$$\hbar \equiv h / 2\pi$$

 

[dextercioby]

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

Daniel.

 

[selfAdjoint]

The Bohr model of the atom is responsable for the "reduction" by $2\pi$ (because the orbits were circular).

Daniel.

And also because the wave function is of the form $$e^{i\phi}$$ which defines the unit circle in the complex plane.

 

[dextercioby]

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

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).

 

[eNathan]

May I ask. What is the purpose of Planks Constant $$p$$anyway? :woundering:

 

[dextercioby]

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.

 

[Reshma]

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

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 $$h$$ as Planck's constant while the latter versions have it as $$\hbar$$.

 

[dextercioby]

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

Daniel.

 

[Reshma]

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

Here is an excerpt:

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

 

[dextercioby]

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.