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.
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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, 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 $\Psi$ in the relevant Hilbert space is given by $i\hbar\partial_t\Psi = \hat{H}\Psi$, where $\hat{H}$ is the linear operator representing the Hamiltonian, usually of the form $-\frac{\hbar^2}{2m}\Delta + V$ where $\Delta$ is the relevant Laplace(-Beltrami) operator.

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