Dynamics of Quantum Particles in Perturbed Parabolic 2d Potential

Authors A.S. Mazmanishvili1 , I.A. Knyaz’2

1 NSC "Kharkov Institute of Physics and Technology", 1, Academicheskaya st., 61108, Kharkov, Ukraine

2 Sumy State University, 2, Rimsky-Korsakov st., 40007 Sumy, Ukraine

Е-mail [email protected]
Issue Volume 8, Year 2016, Number 4
Dates Received 12 February 2016; published online 29 November 2016
Citation A.S. Mazmanishvili, I.A. Knyaz’, J. Nano- Electron. Phys. 8 No 4(1), 04014 (2016)
DOI 10.21272/jnep.8(4(1)).04014
PACS Number(s) 03.65. – w, 02.30.Jr
Keywords Quantum particle, Schrödinger equation (5) , Perturbed potential.
Annotation 2d quantum-mechanical problem of the time evolution of a particle in a quadratic potential is studied. We suppose that the center of the potential is displaced in arbitrary way in time. An analytical expression for the wave function in arbitrary instant time was built. It is shown the dynamic shift of the center of the potential doesn’t change the variance. Moreover, the system can exhibit the resonance: when the frequency of the potential perturbation approaches to the natural frequency the amplitude of the wave packet of particle is increased.

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