Differences

This shows you the differences between two versions of the page.

--- equations:hamilton-jacobi_equation [2018/04/15 11:50]
ida [Abstract]
+++ equations:hamilton-jacobi_equation [2018/05/05 12:29] (current)
63.143.42.253 ↷ Links adapted because of a move operation
@@ Line 15: / Line 15: @@
 <blockquote>The Hamilton-Jacobi equation is essentially a dispersion relation for
 a complex wave. This is easy to see in the context of non-relativistic
-[[theories:quantum_mechanics|quantum mechanics]]. If a quantum amplitude is expressed in the
+[[theories:quantum_mechanics:canonical|quantum mechanics]]. If a quantum amplitude is expressed in the
 form ψ = Rexp(iS/h¯), then the Hamilton-Jacobi equation relates
 p = ∂S/∂q to E = −∂S/∂t by the condition p2(q) = 2m(E −V).
@@ Line 51: / Line 51: @@
 where $p_1$ is the momentum of the particle going from $q_0$ to $q_1$, at time $t_1$, and
-$$  \frac{\partial W}{\partial q_0^i}&= -(p_0)_i,\qquad\text{(-momentum at time $t_0$)} $$
+$$  \frac{\partial W}{\partial q_0^i}= -(p_0)_i ,\qquad\text{(-momentum at time $t_0$)} $$
-$$ \frac{\partial W}{\partial t_1}&= -H_1,\qquad\text{(-energy at time $t_1$)} $$
+$$ \frac{\partial W}{\partial t_1}= -H_1,\qquad\text{(-energy at time $t_1$)} $$
-$$ \frac{\partial W}{\partial t_0}&= H_0,\qquad\text{(+energy at time $t_0$)}
+$$ \frac{\partial W}{\partial t_0}= H_0,\qquad\text{(+energy at time $t_0$)}
  $$