Can the solution of a spinless particle for a Schrodinger equation/Klein Gordon equation be a square wave? If yes, what are those energy potential conditions?
Hello!
The sinc wave packet (e.g, see International Journal of Quantum Chemistry, Vol. 92 (2003) pp. 205-211) has almost a square shape, which seems to be useful for precise, time-dependent reactive scattering calculations.
Cheers,
Alexis
Hi Behnam> Sorry I could not be put in clearly. The difference between square wave like 1, -1, 1, -1 and 1,0,1,0 is that in the former the probability of finding the particle is uniform in the whole universe. On the other hand 1, 0, 1, 0, ... is that it means the particle does not occur at repeated intervals. I agree that potential calculations are simple. My intuition is that it should result in positive and negative delta functions at specific intervals. The question is: does having a 1, 0, 1, 0... kind of square wave makes sense for a particle?
Really, guys? The answer is, "Mathematically, YES -- it only requires an infinite potential," AND, "Physically, NO -- there are no infinite potentials in nature." This is covered in every Introductory Quantum Mechanics course. (Of course, you can get arbitrarily close to a square wave by making a big enough potential at the edge; I suppose for an Engineer that would suffice. :-)
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