Hello,

I have the following question:

Regarding a particle starting out as a Gaussian wave packet G(a, k_0, x, 0) in the setup of a delta potential at x = 0.

Now imagine the particle interpretation: a particle approaches the delta potential in a scattering configuration (E > V_min).

By wave--particle duality, can I instead of working with the Gaussian initial state, deal with the particle configuration with the momentum of the particle being k_0? This can simplify a given problem as we don't have to work with the Gaussian, which at times become much more tedious.

In a problem with a delta potential at x = 0, if a particle starts out with G(a, k_0, x, 0), the transmission coefficient for scattering state can be found exactly the same if we instead deal with the particle interpretation (i.e., solve the problem in the standard way).

In other words, the Gaussian wave packet is isomorphic to the particle setup in a Hilbert space.

Any help would be much appreciated.

Thanks in advance!

Just found out that this approach also works for the step potential!!!!!