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Math Formula Information

Formula: ${\displaystyle \mathrm {i} \hbar {\frac {d}{dt}}|\Psi (t)\rangle ={\hat {H}}|\Psi (t)\rangle }$

Name: Schrödinger equation

Description: partial differential equation describing how the quantum state of a non-relativistic physical system changes with time

Elements of the Formula

imaginary unit	${\displaystyle \mathrm {i} }$	square root of negative one, used to define complex numbers
reduced Planck constant	${\displaystyle \hbar }$	physical constant, Dirac's constant: the Planck constant divided by 2 π; mathematical symbol h-bar ‹ℏ› (U+210F)
duration	${\displaystyle t}$	physical quantity for describing the temporal distance between events
quantum state vector	${\displaystyle |\,\psi (t)\rangle }$	nonzero element of a Hilbert space describing the state of a quantum system
Hamiltonian operator	${\displaystyle {\hat {H}}}$	quantum operator for the energy

Data Source

https://www.wikidata.org/Special:EntityPage/Q165498