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MitsuruYamada

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02-04-2013
08:20 AM

Quantum mechaical indistinguishability of particles. Is it included in the Schroedinger equation?

A very interesting thing was written in a book page 126 of "Quantum Universe" written by Brian Cox & Jeff Forshaw from Penguin books.

Assume there is a pair of identical particles in a space.

One of them has a name "A" and located at x1, the other having name "B" located at x2.

Assume they are interacting.

Then let them start their free motions.

According to the book, as time passes, the identity of the first particle and one of the second particle will mingle.

Reading this, I tried a computer simulation for one dimesional system.( Two dimensional simulation dissipates too much long time.)

I set a parabolic potential as a common potential, and set a Gaussian repulsion potetial for their mutual repulsion.

As a starting waves, I assumed a pair of Gaussioan wave packets placed symmetrically with regard to the origin.

Then I let the usual time-dependent Schroedinger evolution program run.

While running the program, I monitored the density distribution function and two peaks of center of gravity.

But the desired and expected intermingling phenomenon never happned.

Tracing the center of gravities, the particle A continued to be A , the particle B continued to be B completely.

The identities of both particle seemed to be kept independent rigidly.

Oh, my! The story of the book and of my simulation are different!

Where is wrong at all? Or does the usual time-dpendent Schroedinger equation not involve this factor, that is, the factor of the evolution of indistinguishability?

A drifting man on a raft in an ocean named "Quantum World"

February 4, 2013