Ground State of a Quantum Particle in a Potential Field
Abstract
A solution of the Schrödinger equation for the ground state of a particle in a potential field is analyzed. Since the wavefunctions of the ground state are nodeless, potentials of various kinds can be unambiguously determined. It turns out that the ground state corresponds to zero energy for a wide class of model potentials. Moreover, the zero level can be a single one at the boundary of the continuous spectrum. Craterlike potentials monotonically dependent on coordinates in one, two, and threedimensional cases are studied. Instantontype potentials with two local minima are of interest in the onedimensional case. For the Coulomb potential, the energy of the ground state is stable with respect to both long and shortrange screening of this potential. Twosoliton solutions of the nonlinear Schrödinger equation are found. It is demonstrated that the proposed version of the inverse scattering transform is efficient in the analysis of solutions of differential equations.
 Publication:

Soviet Journal of Experimental and Theoretical Physics Letters
 Pub Date:
 September 2020
 DOI:
 10.1134/S002136402014009X
 Bibcode:
 2020JETPL.112..101D