Gaussian wave packet

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

$$ \Psi(x,y,0) = A \exp\left(-\frac{(x-x_0)^2 + (y-y_0)^2}{4\sigma^2}\right) \exp\left(\frac{i}{\hbar}(p_{x0}x + p_{y0}y)\right) $$

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.

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Author of the notes: Antonio J. Pan-Collantes

antonio.pan@uca.es

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