Gaussian Packet

Packet Evolution in Square Potentials

This applet shows the evolution of the evolution of a wave function corresponding to a wave packet in a variety of square potentials. In addition Bohmian particles can be included. These particles appear in Bohmian Mechanics, an interpretation of Quantum Mechanics without observers, originally proposed by Louis de Broglie and David Bohm. Each wave function has only one particle associated with it. However more particles are allowed for illustration. They are evolved following the recipe from Bohmian Mechanics.

There are three regions on the plot. The left most region has a zero potential, so the packet represents a free particle. The potential (V2) and the lenght (L) of the intermediate region can be set on the Parameter panel.

The applet has two panels: Control and Parameters. Use the combo box below the left bottom corner of the graph to switch between them.

Parameter Panel:

The following parameters controlling the wave packet evolution can be adjusted:

K. Energy: Kinetic energy of the wave Packet.
Mass: Mass of the particle.
V2: Potential in the central region.
V3: Potential in the right most region.
L: Length of the central region.

Control Panel:

The following adjustable variables are available:

# Bohm part. : Controls the number of Bohmian particles depicted.
Par. Dist. : Determines how the Bohmian particles are position at the initial time. The distribution can be flat, that is equal distribution in space, or according to the probability determined by the wave function, |Y||Y| (Prob).Particles are distributed in a region of +/- 2 Dx, where Dx is the initial packet width.
Plot: Select whether the real, imaginary or absolute value of the wave function is displayed. At least one of them should be selected.
Time: Sets the time units to be used.
Distance: Sets the distance units to be utilized.

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