Origin of Josephson voltage equation?

i cant find a satisfying explanation, and I cant figure it out myself, a derivation for the josephson equation: $$U(t)=\frac{\hbar}{2e}\frac{d\phi}{dt}$$ where $$U(t)$$ is the voltage, and $$\phi$$ is the phase.

Ive tried looking at the dynamics of the 2 involved superconductors $$a$$ and $$b$$ via the schrödinger equation, by making the ansatz $$\phi_{a/b}=\sqrt n_{a/b} e^{i\theta_{a/b}}$$(i saw in a textbook) but i didnt really get anywhere with this.

• See eq. (3) and (4) in B. D. Josephson paper journals.aps.org/rmp/abstract/10.1103/RevModPhys.46.251 – Alex Trounev May 20 at 16:51
• An explanation here which follows Feynman’s derivation. – Farcher May 20 at 17:30
• @AlexTrounev Your paper that you have cited is behind a pay wall. – Farcher May 20 at 17:32
• @Farcher This is not my paper, this one was written by Josephson. – Alex Trounev May 20 at 17:44
• @AlexTrounev Sorry if my comment attributed the paper to you. My point is that it is not accessible unless one, or the institution one is associated with, subscribes to the journel. – Farcher May 20 at 17:47