# Time Evolution of Squeezed Quantum States of the Harmonic Oscillator

Time Evolution of Squeezed Quantum States of the Harmonic Oscillator

This Demonstration shows the behavior of a minimum-uncertainty (Gaussian) squeezed wave packet for the quantum harmonic oscillator. The squeezing is described by a complex number , with . In polar coordinates, , . The variable determines the magnitude of squeezing and determines the phase angle. There are also the translation controls and . The graphic at the top shows the time evolution of the phase-space Wigner quasi-probability distribution (which is positive definite in this case). The two lower graphics show the time evolution of the -space and the -space probability distributions that can be obtained by integrating the Wigner distribution over momentum or over position , respectively. They exhibit the so called "breathing" phenomenon—periodic change of the width and the height of the wave packet.

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