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==Mathematics==
==Mathematics==
The mathematics of Quantum mechanics can be formulated in a number of ways: the "matrix mechanics" of Werner Heisenberg, the "path integrals" of [[Richard Feynman]], or the "wave mechanics" of Erwin Schrodinger. Wave mechanics is the most common formulation. It uses the language of infinite dimensional [[Hilbert Space]]s; observables such as position and momentum are [[operator]]s on such Hilbert Spaces.
The mathematics of Quantum mechanics can be formulated in a number of ways: the "matrix mechanics" of Werner Heisenberg, the "path integrals" of [[Richard Feynman]], or the "wave mechanics" of Erwin Schrodinger. Wave mechanics is the most common formulation. It uses the language of infinite dimensional [[Hilbert Space]]s; observables such as position and momentum are [[operator]]s on such Hilbert Spaces.
==Postulates of Quantum Mechanics==
*A physical state corresponds to a unit vector <math>\Psi</math> in a Hilbert space.
*Observable physical properties such as position, energy, and momentum are represented by self-adjoint operators on the Hilbert space.
*If we measure an observable <math>Q</math> of a physical state <math>\Psi</math>, the result of our measurement will be an eigenvalue <math>\lambda</math> for the operator <math>Q</math>. The probability that the measurement will yield the value <math>\lambda</math> is given by the norm-squared of the projection of <math>\Psi</math> onto the <math>\lambda</math>-eigenspace of <math>Q</math>.
*If we measure the observable <math>Q</math> and produce the value <math>\lambda</math>, the state <math>\Psi</math> collapses to its projection onto the <math>\lambda</math>-eigenspace of <math>Q</math>.
*A state <math>\Psi</math> evolves in time according the equation: <math>\Psi(t)=e^{iHt}\Psi(0)</math>, where <math>H</math> is the energy operator.
==External Links==
==External Links==