Madelung equations

Madelung equations

The Madelung equations are Erwin Madelung's alternative formulation of the Schrödinger equation.

Equations

The first equation has the form of a continuity equation.

: partial_t ho +frac{1}{m} ablacdot( ho abla S)= 0

The second equation is a Hamilton–Jacobi equation.

: partial_t S +frac{1}{2m}( abla S)^2 +V(x)- frac{hbar^2}{2m} frac{Delta sqrt{ ho{sqrt{ ho= 0

where abla S is interpreted as an impulse.


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