Schrödinger field

In quantum mechanics and quantum field theory, a Schrödinger field, named after Erwin Schrödinger, is a quantum field which obeys the Schrödinger equation. While any situation described by a Schrödinger field can also be described by a many-body Schrödinger equation for identical particles, the field theory is more suitable for situations where the particle number changes. A Schrödinger field is also the classical limit of a quantum Schrödinger field, a classical wave which satisfies the Schrödinger equation. Unlike the quantum mechanical wavefunction, if there are interactions between the particles the equation will be nonlinear. These nonlinear equations describe the classical wave limit of a system of interacting identical particles. The path integral of a Schrödinger field is also known as a coherent state path integral, because the field itself is an annihilation operator whose eigenstates can be thought of as coherent states of the harmonic oscillations of the field modes. Schrödinger fields are useful for describing Bose–Einstein condensation, the Bogolyubov–de Gennes equation of superconductivity, superfluidity, and many-body theory in general. They are also a useful alternative formalism for nonrelativistic quantum mechanics. A Schrödinger field is the nonrelativistic limit of a Klein–Gordon field. A Schrödinger field is a quantum field whose quanta obey the Schrödinger equation. In the classical limit, it can be understood as the quantized wave equation of a Bose Einstein condensate or a superfluid. A Schrödinger field has the free field Lagrangian When is a complex valued field in a path integral, or equivalently an operator with canonical commutation relations, it describes a collection of identical non-relativistic bosons. When is a Grassmann valued field, or equivalently an operator with canonical anti-commutation relations, the field describes identical fermions.