Chocolate-Milk wrote:How did I miss this for like a yearQuarg Ranger wrote:E_0 = ћω/2Chocolate-Milk wrote: I've developed a more efficient system for modding the forum.
I call it 'zero point energy'.
Quarg what does this say
Haha, I came back to the forums today to see this, I've just had 5 lectures on the Quantum Harmonic Oscillator from potential lecturer recruits.
It means that the lowest energy eigenvalue, or ground-state energy, of a quantum system is non-zero. It's the energy associated with the vacuum, also known as 'zero-point energy'. Some people talk about the physical interpretation of it being to do with the Heiesnberg uncertainty principle, because space is ultimately confined, there has to be some energy that the vacuum has. It's interesting stuff.
I could prove it for you in the case of the Quantum Harmonic Oscillator, but that's probably a bit of hassle if you don't know the maths. For a QHO, the ground state energy is E_0 = ћω/2, where E_0 is the ground state energy, ћ is the reduced Planck constant, and ω is the fundamental frequency of that state. It turns out that because every system oscillating around a minimum can be approximated by a Quantum Harmonic Oscillator (because all minima look a little bit like a parabola, mathematically you can see because of a thing called Taylor Series), this is the minimum energy of any Physical state.
The reason Physical states are all minima of energy (i.e. they look like a bowl, rather than an upside-down bowl), is actually really a very important point. It's because it means that things don't get bigger forever (imagine it like a ball in the bowl or on the upside down one, if you put the ball in the bowl, eventually it'll settle, if you put it on the upside-down bowl, then it would carry on rolling away forever, and not only that, it would get faster and faster the further away from the middle you put it. In terms of energy, the first one is Physical, and the second is not (because we don't see things increasing in energy forever). There's some nuance missing there, but that's the general picture.
Probably too much information there. Wikipedia is a good place to reference for more on the vacuum energy stuff if you're interested. They like often to use v (nu) and not ω for frequency, but that's fine (it's left over from the fact that historically, v was used for the quantum mechanics/photoelectric effect stuff by Einstein, Planck etc., and ω is classical frequency things, and then people realised that they're similar things, so started using them interchangeably. Hooray, no standard notation in Physics).