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In physics, the Schrödinger picture or Schrödinger representation is a formulation of quantum mechanics in which the state vectors evolve in time, but the operators (observables and others) are mostly constant with respect to time (an exception is the Hamiltonian which may change if the potential changes).
All three of these choices are valid; the first gives the Schrödinger picture, the second the Heisenberg picture, and the third the interaction picture. The Schrödinger picture is useful when dealing with a time-independent Hamiltonian H , that is, ∂ t H = 0 {\displaystyle \partial _{t}H=0} .
This implies that a Schrödinger picture is always available. Matrix mechanics easily extends to many degrees of freedom in a natural way. Each degree of freedom has a separate X operator and a separate effective differential operator P , and the wavefunction is a function of all the possible eigenvalues of the independent commuting X variables.
The interaction picture is useful in dealing with changes to the wave functions and observables due to interactions. Most field-theoretical calculations [4] use the interaction representation because they construct the solution to the many-body Schrödinger equation as the solution to the free-particle problem plus some unknown interaction parts.
In the Schrödinger picture, the wave function or field is the solution to the Schrödinger equation; = ^ one of the postulates of quantum mechanics. All relativistic wave equations can be constructed by specifying various forms of the Hamiltonian operator Ĥ describing the quantum system .
which is an eigenvalue equation. Very often, only numerical solutions to the Schrödinger equation can be found for a given physical system and its associated potential energy. However, there exists a subset of physical systems for which the form of the eigenfunctions and their associated energies, or eigenvalues, can be found.
It was the first example of quantum dynamics when Erwin Schrödinger derived it in 1926, while searching for solutions of the Schrödinger equation that satisfy the correspondence principle. [1] The quantum harmonic oscillator (and hence the coherent states) arise in the quantum theory of a wide range of physical systems. [2]
In the framework of the de Broglie–Bohm theory, the quantum potential is a term within the Schrödinger equation which acts to guide the movement of quantum particles. . The quantum potential approach introduced by Bohm [1] [2] provides a physically less fundamental exposition of the idea presented by Louis de Broglie: de Broglie had postulated in 1925 that the relativistic wave function ...