Normal Mode - Quantum Mechanics

Quantum Mechanics

In quantum mechanics, a state of a system is described by a wavefunction which solves the Schrödinger equation. The square of the absolute value of, i.e.

$\ P(x,t) = |\psi (x,t)|^2$

is the probability density to measure the particle in place x at time t.

Usually, when involving some sort of potential, the wavefunction is decomposed into a superposition of energy eigenstates, each oscillating with frequency of . Thus, we may write

$|\psi (t) \rang = \sum_n |n\rang \left\langle n | \psi ( t=0) \right\rangle e^{-iE_nt/\hbar}$

The eigenstates have a physical meaning further than an orthonormal basis. When the energy of the system is measured, the wavefunction collapses into one of its eigenstates and so the particle wavefunction is described by the pure eigenstate corresponding to the measured energy.

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