# Potential well& wave packet

1. Jul 11, 2008

### shubhajit

1.in the attached file see the fig 8.5 What is the the physical reason,for which ahe amplitude of the wave function is larger in between x=0 & x= a ?
2.what is the reason for choosing a wave packet to describe a particle ?

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2. Jul 11, 2008

### malawi_glenn

1) because of the mathematics - you'll get a so called resonance.

2) google "history of quantum mechanics" and similar.

3. Jul 11, 2008

### Staff: Mentor

To elaborate on malawi_glenn's response, notice that the width of the barrier is 2.5 times the wavelength, for this particular E. A wave coming in from the left is partially reflected at each side. After reflecting at the right side and then again at the left side, it's exactly 5 wavelengths shifted with respect to the wave that has just passed through the left side... so the two waves are in phase and we have constructive interference.

For other barrier energies you can have destructive interference which produces a reduced amplitude inside the barrier.

A single wave with a completely definite wavelength and frequency is unphysical, because it must extend to infinity and therefore cannot be normalized to yield a total probablity of 1. In order to get a free-particle wave function that is finite in extent and can be normalized, we have to add (integrate) an infinite number of waves, with a range of wavelengths.