Quantum foam

[serunato]

Somebody just threw an equation at me and called it something like Planck's equation for energy in a vacuum: E=(1/2+n)h_bar w.

Where n is the number of photons and w is the frequency, should be nu.

Anybody heard of such a thing or is it pure BS? I know Planck's equation:

E=hv

But I never seen this stuff.

[Martin]

Somebody just threw an equation at me and called it something like Planck's equation for energy in a vacuum: E=(1/2+n)hbar w.

Where n is the number of photons and w is the frequency' date=' should be nu.

Anybody heard of such a thing or is it pure BS? I know Planck's equation:

E=hv

But I never seen this stuff.[/quote']

 

[math]\hbar = \frac{h}{2\pi} [/math]

 

A lot of people use w as a substitute for little omega

the conventional symbol for the "angular" frequency

(think of it as radians per second instead of cycles per second, so the same frequency can be be described in two different formats, angular or cyclic)

 

[math]\omega = 2\pi \nu [/math]

 

hbar is the form of planck's constant which you use when you are writing frequency as omega----in angular format.

 

[math]E = \hbar \omega [/math]

 

you might find this hard to believe but the first occurrence of Planck's constant, in Planck's writing, was a constant equal to hbar!

that came in 1899 (he wrote a different symbol for it, not hbar)

and only in 1900 did he bring out the constant h, which was larger by a factor of 2 pi.

 

In advanced quantum mechanics and quantum field theory courses you will commonly see hbar. And frequencies very commonly are in angular format. this may seem wrong to you but it works out a bit cleaner in a lot of situations. maybe in the end it is on balance a bit more natural and convenient. People's taste varies of course

 

this equation

[math]E = \hbar \omega [/math]

 

is EXACTLY the same as this equation

[math]E = h \nu [/math]

 

It is only in a different format.

To get back from one to the other,

you just have to chop a factor of 2 pi out of the h

and put it into the nu.

E doesnt change, and you get the other equation back.

 

If you want to see how the greek letters are written, press "quote" on this post and it will give you the source----what you have to type in order to get omega and hbar etc.

[swansont]

Somebody just threw an equation at me and called it something like Planck's equation for energy in a vacuum: E=(1/2+n)h_bar w.

Where n is the number of photons and w is the frequency' date=' should be nu.

Anybody heard of such a thing or is it pure BS? I know Planck's equation:

E=hv

But I never seen this stuff.[/quote']

 

yes. It's the QM solution for a harmonic oscillator