General form the Schrodinger Equation: dPsi/dt = -iH/hbar Psi
Quantum Field theories are not usually presented in this form because it’s intrinsically nonrelativistic, but if you pick a reference frame, you can dump the time derivative on the left and everything else on the right as part of H and there you go.
So it’s equivalent. As calef says, there are good reasons not to actually do anything with it in that form.
This is a little chicken-or-the-egg in terms of “what’s more fundamental?”, but nonrelativistic QFT really is just the Schrodinger equation with some sparkles.
For example, the language electronic structure theorists use to talk about electronic excitations in insert-your-favorite-solid-state-system-here really is quantum field theoretic—excited electronic states are just quantized excitations about some vacuum (usually, the many-body ground state wavefunction).
You could switch to a purely Schrodinger-Equation-motivated way of writing everything out, but you would quickly find that it’s extremely cumbersome, and it’s not terribly straightforward how to treat creation and annihilation of particles by hand.
QFT is a special case of the general form of the Schrodinger equation.
Link?
General form the Schrodinger Equation: dPsi/dt = -iH/hbar Psi
Quantum Field theories are not usually presented in this form because it’s intrinsically nonrelativistic, but if you pick a reference frame, you can dump the time derivative on the left and everything else on the right as part of H and there you go.
So it’s equivalent. As calef says, there are good reasons not to actually do anything with it in that form.
This is a little chicken-or-the-egg in terms of “what’s more fundamental?”, but nonrelativistic QFT really is just the Schrodinger equation with some sparkles.
For example, the language electronic structure theorists use to talk about electronic excitations in insert-your-favorite-solid-state-system-here really is quantum field theoretic—excited electronic states are just quantized excitations about some vacuum (usually, the many-body ground state wavefunction).
Another example: http://en.wikipedia.org/wiki/Kondo_model
You could switch to a purely Schrodinger-Equation-motivated way of writing everything out, but you would quickly find that it’s extremely cumbersome, and it’s not terribly straightforward how to treat creation and annihilation of particles by hand.