Schrödinger equation: Difference between revisions
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The '''Schrödinger equation''' is one of the fundamental equations of quantum mechanics and describes the spatial and temporal behavior of quantum-mechanical systems. [[Austrian]] [[physicist]] [[Erwin Schrödinger]] first proposed the equation in early 1926. | The '''Schrödinger equation''' is one of the fundamental equations of quantum mechanics and describes the spatial and temporal behavior of quantum-mechanical systems. [[Austrian]] [[physicist]] [[Erwin Schrödinger]] first proposed the equation in early 1926. | ||
Mathematically, the Schrödinger equation is an example of an [[eigenvalue problem]] whose eigenvectors are called "wavefunctions" or "quantum states" and whose eigenvalues correspond to [[energy level|energy levels]]. Built into the eigenvectors are the probabilities of measuring all values of all physical [[observable|observables]], meaning that a solution of the Schrödinger equation provides a complete physical description of a | Mathematically, the Schrödinger equation is an example of an [[eigenvalue problem]] whose eigenvectors are called "wavefunctions" or "quantum states" and whose eigenvalues correspond to [[energy level|energy levels]]. Built into the eigenvectors are the probabilities of measuring all values of all physical [[observable|observables]], meaning that a solution of the Schrödinger equation provides a complete physical description of a system. The equation can be written in terms of [[Hamiltonian|Hamiltonians]] for both classical and quantum mechanical systems; in the latter case, the Hamiltonian functions are replaced by Hamiltonian operators. | ||
==Time-independent Schrödinger Equation== | |||
[[Louis de Broglie|De Broglie]] postulated that associated with every particle is a particular wavelength defined by | |||
<math>\lambda = h/p</math> | |||
[[Category:CZ Live]] | [[Category:CZ Live]] | ||
Revision as of 21:43, 9 February 2007
The Schrödinger equation is one of the fundamental equations of quantum mechanics and describes the spatial and temporal behavior of quantum-mechanical systems. Austrian physicist Erwin Schrödinger first proposed the equation in early 1926.
Mathematically, the Schrödinger equation is an example of an eigenvalue problem whose eigenvectors are called "wavefunctions" or "quantum states" and whose eigenvalues correspond to energy levels. Built into the eigenvectors are the probabilities of measuring all values of all physical observables, meaning that a solution of the Schrödinger equation provides a complete physical description of a system. The equation can be written in terms of Hamiltonians for both classical and quantum mechanical systems; in the latter case, the Hamiltonian functions are replaced by Hamiltonian operators.
Time-independent Schrödinger Equation
De Broglie postulated that associated with every particle is a particular wavelength defined by
