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.
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.