Friday, 5 June 2015

homework and exercises - How do you get quantum Hamilton-Jacobi equation from Schrödinger equation?



I am reading "The undivided universe: an ontological interpretation of quantum theory" and cannot understand this derivation.


From the Schrödinger equation: $$ i\hbar \frac{\partial\psi}{\partial t} = -\frac{\hbar^2}{2m}\nabla^2\psi + V\psi $$ They derive the quantum Hamilton-Jacobi equation $$ \frac{\partial S}{\partial t} + \frac{(\nabla S)^2}{2m} + V + Q = 0 $$



using the polar form $\psi = Re^{iS/\hbar}$, but I don't understand what they do afterwards.




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