Gaussian Wave Packet: Reflection & Transmission

[h0dgey84bc]

If you imagine a string, the first part of the string (that the gaussian looking wave peak is moving along) has thicker mass density than the latter part of the string. (so it's essentially a thick bit of string going on to a thinner bit).
What would happen when the wavepacket reaches the latter section? I think you will get an upright reflected wavepacket and also an upright transmitted wavepacket, is this correct?
(the reason I think this is because I'm thinking it's like the wavefunction of a free particle, colliding with a stationary particle of lower mass, so it's analogous to an elastic collision?)

Thanks

 

[jtbell]

I think you will get an upright reflected wavepacket and also an upright transmitted wavepacket, is this correct?

Yes. If the packet goes enters from the other direction, and goes from the "light" string to the "heavy" string, the reflected packet is inverted. I've done this as a demonstration in intro physics classes.

You have something similar in optics. Light reflecting off a air-to-glass boundary (from outside the glass) is phase shifted by half a cycle, but not when reflecting off a glass-to-air boundary (from inside the glass). Here what matters is whether the index of refraction increases or decreases as you go across the boundary.

 

[h0dgey84bc]

thanks, I like the optics comparison, shall help me remember the order.