Are there any nice wave packets you could write as a superposition of eigenstate solutions of a one-dimensional harmonic oscillator? The question deals with a situation, where a particle feels a harmonic potential, but is far away from the center and is travelling as a wave packet, probably oscillating like a classical particle before spreading.(adsbygoogle = window.adsbygoogle || []).push({});

I tried the usual gaussian wave packet, but it lead to an integral

[tex]

\int\limits_{-\infty}^{\infty} H_n(x) e^{-Ax^2+Bx}dx

[/tex]

which I found too difficult for myself. Do you know if a foolproof technique already exists for integrating this, or if there is other kind of wave packets that are easier?

[tex]H_n[/tex] is Hermite's polynomial.

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# Wave packets that feel harmonic potential

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