On The effects of non-Gaussian wave packets on double slit interference patterns

A parametric comparison of Lorentzian wavepackets versus Gaussian wavepackets in double-slit experiments, using computational analysis.

Abstract

Wavepackets, defined as a superposition of plane waves with finite spectral width and spatial localisation arising from Fourier structure, are essential in both relativistic and non-relativistic setups in quantum theory. Different wave packets can be made by altering the functional form of the envelope of the wave packet. For the double slit experiment, non-matter waves are usually preferred to be modelled by the Gaussian wavepacket because they allow closed-form solutions under the Fourier transformation, which simplifies the prediction of interference effects. Hence, there is an existing gap in the current literature on the effects on double slit interference patterns when non-Gaussian wavpackets, such as the Lorentzian wavepacket, are used.

The study thus examined the effects of non-Gaussian wavepackets by comparing the interference patterns by modelling the interference patterns at a screen, D distance away. The study used 'condition sets', with varied parameters in each set to model interference in different geometric setups (varying geomteric factors like slit separation, wave number, and the width of wavepackets). The interference patterns were then analysed at different 'time-frames' (considering time as a paramteric index but not physical time) to observe the evolution of the interference patterns.

The results showed stark differences; Gaussian and Lorentzian wavepackets had clear and systematic differences in how they evolve and form double-slit interference pattern. Gaussian packets transitioned from a single central maximum to two dominant peaks with time, with larger slit separations producing this transition earlier and yielding more fringes overall, whereas Lorentzian packets, with their heavy tails, evolved faster; secondary maxima became competitive earlier, fringe amplitudes persisted farther out, and an unusual three-peak structure emerged under specific low-distance conditions.

Overall, the results show that wavepacket shape strongly influences early-time interference features, while the large-scale structure is controlled primarily by slit geometry and wavelength.