KevinYager: /* Example: Oscillation in Stationary State */

2014-11-04T13:55:57Z

‎Example: Oscillation in Stationary State

KevinYager: Created page with "Particles in quantum mechanics can be thought of as wave packets that evolve in time according to the Quantum_mechanics#Schr.C3.B6dinger_Equation|Schrödinger Equati..."

2014-11-04T13:53:18Z

Created page with "Particles in quantum mechanics can be thought of as wave packets that evolve in time according to the Quantum_mechanics#Schr.C3.B6dinger_Equation|Schrödinger Equati..."

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Particles in [[quantum mechanics]] can be thought of as [[wave packet]]s that evolve in time according to the [[Quantum_mechanics#Schr.C3.B6dinger_Equation|Schrödinger Equation]]. Even in cases where the square of the wavefunction (<math>\scriptstyle |\psi(x)|^2 </math>) appears static ("stationary states"), the complex amplitude of the wavefunction (<math>\scriptstyle \psi(x)</math>) is in fact varying in time. In particular, the form of the time-dependent Schrödinger Equation demands that the amplitude oscillate (roughly, the amplitude oscillates between the real and imaginary components; i.e. the vector in the complex plane rotates continuously).

==Example: Propagation and Interaction==
Wave-packets can propagate, frequently with dispersion (which induces spatial spread of the envelope). Wave-packets can interact with barriers (defined by, e.g., some potential function), and interfere with themselves.

{|
| [[Image:Wavepacket-Box-wavefunc3.gif|500px|thumb|Components of the wavefunction (<math>\scriptstyle \psi(x) </math>) describing a wave-packet bouncing inside a box-like potential. The black line is the real part, and the blue line is the imaginary part.]]
|-
| [[Image:Wavepacket-Box-sqr2.gif|500px|thumb|Square of the wavefunction (<math>\scriptstyle | \psi(x) |^2 </math>) for a wave-packet bouncing inside a box-like potential.]]
|}

==Example: Oscillation in Stationary State==
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Extra:Quantum wave time evolution example - Revision history

KevinYager: /* Example: Oscillation in Stationary State */

KevinYager: Created page with "Particles in quantum mechanics can be thought of as wave packets that evolve in time according to the Quantum_mechanics#Schr.C3.B6dinger_Equation|Schrödinger Equati..."