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# Section 14.6: Exploring Molecular and Nuclear Wave Packets

Molecular Packet | Nuclear Packet

Please wait for the animation to completely load.

This Exploration shows the *same* initial Gaussian wave packet in either a double anharmonic oscillator well or a finite well created to depict molecular or nuclear wave packets, respectively. Specifically,

**One-dimensional Double Well**: An anharmonic oscillator with an added negative harmonic oscillator piece, *V*(*x*) = *V*_{0}*x*^{4 }− 10*V*_{1}*x*^{2}. This double well can be used as a model for the ammonia molecule, NH_{3}. In this molecule, the three hydrogen atoms form an equilateral triangle and the nitrogen atom oscillates through the plane of the hydrogen atoms forming a pyramid shape. The potential energy function the nitrogen experiences in its oscillations is modeled relatively well by this double well potential.

**Radial Finite Well**: A finite well with a Coulomb * tail*, *V*(*r*) = −*V*_{0} for *r* < *a* and *V*(*r*) is proportional to 1/*r* for *r* > *a*. This well can serve as a model for an alpha particle in a nucleus.

- For the molecular wave packet animation, what happens to the packet over time? What do you notice about how the wave function behaves when
*E*<*V*and*E*>*V*? What do you notice about the probability for*x*< 0 and*x*> 0? - For the nuclear wave packet animation, what happens to the packet over time? What do you notice about the probability for
*x*< 2 and*x*> 2? Can you extrapolate to what will happen to the probability of*x*> 2 over time?

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