Square Wave Packet

Square Wave Packet in quantum mechanics is a highly artificial concept, a localised wave packet representing a uniform probability of observing a particle within a specific spatial width a, and zero probability of being found outside the region. The wave packet can be shown to obey the uncertainty principle. The square wave packet is analysed by the Fourier decomposition method.

Equations

The general equation of the wave function for the Square Wave Packet, at time t=0 may be written as

${\psi }_0(x)=\{\begin{array}{ll}A{\exp }^{i{k}_{0}x},& \text{for }|x|\le a\\ 0,& \text{for }|x|>a\end{array}$

Where A is known as normalization factor. The normalization factor A is obtained by the integration of the wave function from x=-a to x=a. For normalization, the integration of the probability function is taken 1.

After integration, the normalization factor is obtained as

$A=1/\surd 2a$

References

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