In Quantum Mechanics (QM), the Planck's constant has the S.I. units of
(energy) x (time). So, how should one interpret that?!
How should I understand the physical meaning of the following relations?
$\frac E \nu = h$
as the "energy content" divided by the "fastness'' of oscillation equals h.
or in terms of the de Broglie definition
$ |\vec{p}| \times \lambda= h$
i.e. particle momentum times the ``size'' of wavelength equals h.
I know that the definitions are linked. However, for the sake of basic understanding, two questions
a) Should I understand that the size of the wavelength is $\underline{\text{fixed}}$ w.r.t the momentum of the particle and similarly its energy fixes the fastness of its oscillations? They are one and the same thing being looked at from different perspective?
b) Is there any classical version of a physical constant that has more than one definition like the Planck's constant?