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SUMMARY:M. I. Tribelsky (Faculty of Physics\, M. V. Lomonosov Moscow State
  University)
DTSTART:20211111T110000Z
DTEND:20211111T120000Z
DTSTAMP:20260423T022835Z
UID:mmandim/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/29/"
 >Fall of Quantum Particle to the Center: Exact solution</a>\nby M. I. Trib
 elsky (Faculty of Physics\, M. V. Lomonosov Moscow State University) as pa
 rt of Mathematical models and integration methods\n\n\nAbstract\nA fall of
  a particle to the center of a singular potential is one of a few fundamen
 tal problems of quantum mechanics. Nonetheless\, its solution is not compl
 ete yet. The known results just indicate that if the singularity of the po
 tential is strong enough\, the spectrum of the Schrodinger equation is not
  bounded from below. However\, the wave functions of the problem do not ad
 mit the limiting transition to the ground state. Therefore\, the unbounded
 ness of the spectrum is only a necessary condition. To prove that a quantu
 m particle indeed can fall to the center\, a wave function describing the 
 fall should be obtained explicitly. This is done in the present paper. Spe
 cifically\, an exact solution of the time-dependent Schrodinger equation c
 orresponding to the fall is obtained and analyzed. A law for the collapse 
 of the region of the wave function localization to a single point is obtai
 ned explicitly. It is shown that the known necessary conditions for the pa
 rticle to fall simultaneously are sufficient.\n
LOCATION:https://researchseminars.org/talk/mmandim/29/
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