- #1
jostpuur
- 2,116
- 19
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 traveling as a wave packet, probably oscillating like a classical particle before spreading.
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.
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.