how do you model numerically the absorption or reflection of a wave-function ?

[Widdekind]

imagine a double-slit experiment w/o the slit...

 

i.e. a blob-like electron wave-function is projected towards a detector...

 

imagine that the detector absorbs 90% of incident electrons, and reflects 10%...

 

you mathematically model the physics on a computer, with a fully 3D computer simulation...

 

the blob-like electron wave-function is some 3D lego-like blocky cellularized shape, occupying some swath of the 3D grid "voxel" cells...

 

the discretized wave-function propagates towards the detector, time-step by time-step...

 

eventually, the "front" of the wave-function reaches the detector...

 

the first such grid "voxel" cell, at the detector, to be (partially) filled with (some) wave-function, has some percent of the particle present, [math]P \equiv \Psi^{*} \Psi dV \ll 1[/math]

 

embodying some amount of momentum, [math]\vec{p} \equiv \Psi^{*} \hat{p} \Psi dV[/math]

 

Q: is the following the appropriate procedure ??

 

probability the particle is absorbed = P x 90% << 1 => wave-function collapse, into classical particle-like state, absorbed into that spot on detector, which absorbs momentum [math]\vec{p}[/math]

probability the particle is reflected = P x 10% << 1 => wave-function collapse, into classical particle-like state, reflected from that spot on detector, which reflects momentum [math]\vec{p}[/math]

 

else, with probability 1-P = 1 - 0.9P - 0.1P, no collapse occurs, no classicality occurs, that piece of the blob of the wave-function merely reflects from that spot, still as a quantum wave, as if that spot of the detector was simply some infinite potential barrier ?

 

then, time-step by time-step, as more and more of the discretized wave-function impacts the detector, you repeat this procedure (??), each "voxel" grid cell's worth of wave-function, gets its chance, to usher in the absorption of the whole particle (90% P_i), to usher in the reflection of the whole particle (10% P_i), or to merely remain as wave-function, reflecting from the spot, as a quantum wave (1-P_i) ?

 

hypothetically, the whole discretized wave-function could fail to absorb classically, and fail also to reflect classically, and so merely reflect as a quantum wave... in which scenario, the blob-like blocky discretized wave-function would wind up evolving / propagating away from the detector, back towards where it originated... ??

[EdEarl]

I believe you know lots more about this subject than I, but sometimes interaction with anyone, regardless of their ignorance can help.

 

A blob is not my image of an electron. There are two, either a string-wave or point-wave. I will not elaborate on the string. My image of a point wave is as a pebble dropped in a pond, except a standing wave that moves in a line instead of the concentric circles expanding from the center. My mind's image of a point-wave electron is similar to the following picture of a hydrogen atom, except without the red and yellow in the middle.

 

http://www.google.com/imgres?client=firefox-a&hs=vJf&sa=X&rls=org.mozilla:en-US:official&tbm=isch&tbnid=jwtUvaSFESNvEM:&imgrefurl=http://www.foxnews.com/science/2013/05/28/amazing-first-ever-photograph-inside-hydrogen-atom/&docid=XxmOMqgGK6tThM&imgurl=http://global.fncstatic.com/static/managed/img/Scitech/image%252520of%252520hydrogen%252520atom.jpg&w=660&h=371&ei=p9TeUZm8JrPNywHazYCgBg&zoom=1&ved=1t:3588,r:0,s:0,i:81&iact=rc&page=1&tbnh=168&tbnw=300&start=0&ndsp=11&tx=254&ty=85&biw=1173&bih=575

Edited July 11, 2013 by EdEarl