# How would a Lagrangian be used to recover the Schrodinger equation?

I heard that the Lagrangian is defined in the path integral formulation of quantum mechanics. How would the Lagrangian in this formulation be used to recover the Schrodinger equation that we normally use?

• Googling "path integrals in quantum mechanics" will give you many sources, for example en.wikipedia.org/wiki/Path_integral_formulation If you have difficulty following the standard presentation please ask another question :) Mar 2, 2013 at 9:06
• The derivation in the link shows how you get from a solution of the Schrödinger equation to the path intergral formalism, but not the other way around. In this sense, the question is not really answered by it. Mar 2, 2013 at 9:35
• This is probably what you're looking for: users.physik.fu-berlin.de/~kleinert/kleiner_re242/node2.html
– Jold
Mar 2, 2013 at 9:59
• Duplicate: physics.stackexchange.com/q/69982 Jul 27, 2013 at 9:26

$\cal{L}=\Psi^{t}(i\frac{\partial}{\partial t}+\nabla^2/2m)\Psi$
$\frac{\partial\cal{L}}{\partial\Psi^t}=0$
The second term of the Lagrange-equation (derivative with respect to $\partial_{\mu}\Psi^t$) is zero since no derivative of $\Psi^t$ occurs in our field Lagrangian density .