2 ms·
I don't think your explanation hits the bottom of the ontic causal hierarchy. The fact that hbar is the quantum of angular momentum can be derived from the bou
by wyager 2y ago
I don't think your explanation hits the bottom of the ontic causal hierarchy.
The fact that hbar is the quantum of angular momentum can be derived from the boundary conditions of a wavefunction with a closed dimension (such as an angle), combined with the fact that one h of action phases a wavefunction by 360º.
In particular, for a wavefunction with only angular dependence:
boson: \psi(2pi) = \psi(0)
fermion: \psi(4pi) = \psi(0)
Because the value has to be the same when you get back to where you started.
Therefore, (for a boson) psi must decompose into eigenfunctions of the form \psi(\theta) = exp(i * n * \theta) where n is an integer.
These eigenfunctions satisfy the boundary condition stated above and are a complete basis
We can take the fourier transform of this (closed) function and we get a dirac delta at n. I.e. the fourier transforms of this basis are just dirac deltas at integers in the fourier domain.
But to convert this to physical units, we need to use the embedding from integers to reals, which is done by multiplication by planck's constant.
So, some related questions that I think are further down the causal hierarchy:
* Why does one h of action phase a wavefunction by 360º
* Why does h necessarily show up in the fourier transform