- #1
Philip Koeck
- 719
- 198
- TL;DR Summary
- If the total energy is proportional to the frequency the results are strange in the limit of small velocities
The relationships for matter waves are (see e.g. https://en.wikipedia.org/wiki/Matter_wave):
λ = h / p and E = h f, where E = m c2
From this the phase velocity can be derived and we get vph = c2 / v.
v is the group velocity, which is also the velocity of the particle.
If I consider these expressions in the limit of v→0 (and p→0), I find that both λ and vph become infinite, whereas f remains finite.
So, a stationary particle with mass still has a finite frequency, but infinite wavelength and phase velocity!
If I, however, decide that Ekin = h f, where Ekin = m v2/2, I find that λ becomes infinite, f becomes zero and vph also becomes zero at the limit of v = 0.
Actually vph = v/2 for all non-relativistic velocities, in that case.
Somehow the latter would feel more natural.
What is the evidence or the reason that the energy in E = h f has to be m c2?
(And what is a stationary particle doing with a frequency?)
λ = h / p and E = h f, where E = m c2
From this the phase velocity can be derived and we get vph = c2 / v.
v is the group velocity, which is also the velocity of the particle.
If I consider these expressions in the limit of v→0 (and p→0), I find that both λ and vph become infinite, whereas f remains finite.
So, a stationary particle with mass still has a finite frequency, but infinite wavelength and phase velocity!
If I, however, decide that Ekin = h f, where Ekin = m v2/2, I find that λ becomes infinite, f becomes zero and vph also becomes zero at the limit of v = 0.
Actually vph = v/2 for all non-relativistic velocities, in that case.
Somehow the latter would feel more natural.
What is the evidence or the reason that the energy in E = h f has to be m c2?
(And what is a stationary particle doing with a frequency?)