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Section 14.6: Exploring Molecular and Nuclear Wave Packets



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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) = V0x4 − 10V1x2.  This double well can be used as a model for the ammonia molecule, NH3.  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) = −V0 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.

  1. 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?
  2. 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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