Quantum mnechanics with lagrangians?...

[eljose79]

usually quantum mechanics is made with hamiltonians but..could it be done with lagrangians in the sense that LF=gF where F is the wave function and g plays a role of an eigenvalue what would happen with

dq/dtF?..in fact would it be equal to qEnF where En is the energy..

this can be useful for the case we have got a lagrangian but its HGamiltonian is H=0 so we can have some troubles it would be very useful for general relativity too......

[GRQC]

Originally posted by eljose79

this can be useful for the case we have got a lagrangian but its HGamiltonian is H=0 so we can have some troubles it would be very useful for general relativity too......

Certainly you can. Everything can be expressed as lagrangians. Quantum field theory is based on lagrangian mechanics, as are certain aspects of gravitation (the Einstein-Hilbert action).

[eljose79]

yes you can but you still have the problem of velocities..for example in Hamiltonian Formulation you have
qF=qF and pF=-ihbardF/dx

but in Lagrangian mechanics..you don,t have momenta but velocities and how could you cope with expresions of the form

dq/dtF=?F perhaps that,s one of the main troubles of Lagrangian version of it....