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The equation was postulated by Schrödinger based on a postulate of Louis de Broglie that all matter has an associated matter wave. The equation predicted bound states of the atom in agreement with experimental observations. [4]: II:268 The Schrödinger equation is not the only way to study quantum mechanical systems and make predictions.
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 .
The Schrödinger equation determines how wave functions evolve over time, and a wave function behaves qualitatively like other waves, such as water waves or waves on a string, because the Schrödinger equation is mathematically a type of wave equation. This explains the name "wave function", and gives rise to wave–particle duality.
and this is the Schrödinger equation. Note that the normalization of the path integral needs to be fixed in exactly the same way as in the free particle case. An arbitrary continuous potential does not affect the normalization, although singular potentials require careful treatment.
In particular, he is recognized for postulating the Schrödinger equation, an equation that provides a way to calculate the wave function of a system and how it changes dynamically in time. Schrödinger coined the term " quantum entanglement ", [ 4 ] [ 5 ] [ 6 ] and was the earliest to discuss it, doing so in 1932. [ 7 ]
The matter wave interpretation was placed onto a solid foundation in 1928 by Hans Bethe, [31] who solved the Schrödinger equation, [16] showing how this could explain the experimental results. His approach is similar to what is used in modern electron diffraction approaches.
In quantum mechanics, the Schrödinger equation describes how a system changes with time. It does this by relating changes in the state of the system to the energy in the system (given by an operator called the Hamiltonian). Therefore, once the Hamiltonian is known, the time dynamics are in principle known.
If the wave function merely encodes an observer's knowledge of the universe, then the wave function collapse corresponds to the receipt of new information. This is somewhat analogous to the situation in classical physics, except that the classical "wave function" does not necessarily obey a wave equation.