2002/06/25 by М. Н. Сергеенко, M. N. Sergeenko, Sergeenko, M. N. · 1 citation
Physics and Astronomy · #FOS: Physical sciences #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0206179
Latex, 20 pages
arxiv created 2002/06/25 · openalex publication_date 2002/06/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Solution of the Schrödinger's equation in the zero order WKB approximation is analyzed. We observe and investigate several remarkable features of the WKB0 method. Solution in the whole region is built with the help of simple connection formulas we derive from basic requirements of continuity and finiteness for the wave function in quantum mechanics. We show that, for conservative quantum systems, not only total energy, but also momentum is the constant of motion. We derive the quantization conditions for two and more turning point problems. Exact energy eigenvalues for solvable and some ``insoluble'' potentials are obtained. The eigenfunctions have the form of a standing wave, Ancos(knx+δn), and are the asymptote of the exact solution.