Difference between revisions of "Schrodinger Equation"
(New page: In the Schrodinger picture, the equation governing quantum mechanical evolution of some state <math>\Psi</math> in the relevant Hilbert space is given by <math>i\hbar\partial_t\Psi = \hat{...) |
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| − | In the Schrodinger picture, the equation governing quantum mechanical evolution of some state <math>\Psi</math> in the relevant Hilbert space is given by <math>i\hbar\partial_t\Psi = \hat{H}\Psi</math>, where <math>\hat{H}</math> is the linear operator representing the Hamiltonian. | + | In the Schrodinger picture, the equation governing quantum mechanical evolution of some state <math>\Psi</math> in the relevant Hilbert space is given by <math>i\hbar\partial_t\Psi = \hat{H}\Psi</math>, where <math>\hat{H}</math> is the linear operator representing the Hamiltonian, usually of the form <math>-\frac{\hbar^2}{2m}\Delta + V</math> where <math>\Delta</math> is the relevant Laplace(-Beltrami) operator. |
Revision as of 16:57, 20 June 2008
In the Schrodinger picture, the equation governing quantum mechanical evolution of some state 
in the relevant Hilbert space is given by 
, where 
is the linear operator representing the Hamiltonian, usually of the form 
where 
is the relevant Laplace(-Beltrami) operator.
