Gaussian wave packet

In a 2 spatial dimension context, a Gaussian wave packet is an initial condition for the Schrodinger equation represented as:

Where:

• $A$ is the normalization constant.
• $\sigma$ is the width of the Gaussian packet.
• $(x_0,y_0)$ is the initial position of the center of the packet.
• $(p_{x0},p_{y0})$ are the initial momenta in the x and y directions.