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The time-dependent Schrödinger equation described above predicts that wave functions can form standing waves, called stationary states. These states are particularly important as their individual study later simplifies the task of solving the time-dependent Schrödinger equation for any state. Stationary states can also be described by a ...
In quantum mechanics and scattering theory, the one-dimensional step potential is an idealized system used to model incident, reflected and transmitted matter waves.The problem consists of solving the time-independent Schrödinger equation for a particle with a step-like potential in one dimension.
The Hartree–Fock method is typically used to solve the time-independent Schrödinger equation for a multi-electron atom or molecule as described in the Born–Oppenheimer approximation. Since there are no known analytic solutions for many-electron systems (there are solutions for one-electron systems such as hydrogenic atoms and the diatomic ...
The problem consists of solving the one-dimensional time-independent Schrödinger equation for a particle encountering a rectangular potential energy barrier. It is usually assumed, as here, that a free particle impinges on the barrier from the left.
In mathematical physics, a Pöschl–Teller potential, named after the physicists Herta Pöschl [1] (credited as G. Pöschl) and Edward Teller, is a special class of potentials for which the one-dimensional Schrödinger equation can be solved in terms of special functions.
The time-independent Schrödinger equation (TISE) is, ^ | = | , where denotes a real number (which needs to be determined) that will specify a time-independent energy level, or eigenvalue, and the solution | denotes that level's energy eigenstate.
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.
A stationary state is a quantum state with all observables independent of time. It is an eigenvector of the energy operator (instead of a quantum superposition of different energies). It is also called energy eigenvector, energy eigenstate, energy eigenfunction, or energy eigenket.