Tunnel splitting of the spectrum and bilocalization of eigenfunctions in an asymmetric double well

DOI10.1007/s11232-014-0132-7zbMath1298.81089OpenAlexW2011018497MaRDI QIDQ461585

E. V. Vybornyi

Publication date: 13 October 2014

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11232-014-0132-7

zbMATH Keywords

semiclassical approximationtunnelingone-dimensional Schrödinger equationquasi-intersection of energy levels

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) (2)-body potential quantum scattering theory (81U05) First-order hyperbolic systems (35L40)

Related Items (6)

Global asymptotics for functions of parabolic cylinder and solutions of the Schrödinger equation with a potential in the form of a nonsmooth double well ⋮ Bi-states and 2-level systems in rectangular Penning traps ⋮ Bi-orbital states in hyperbolic traps ⋮ Energy splitting in dynamical tunneling ⋮ Non-Lie top tunneling and quantum bilocalization in planar Penning trap ⋮ Quantum states of the Kapitza pendulum

Cites Work

• Quantum tunneling in complex systems. The semiclassical approach.
• Semiclassical analysis of low lying eigenvalues. IV. The flea on the elephant
• New approach to the semiclassical limit of quantum mechanics. I: Multiple tunnelings in one dimension
• Splitting of the lowest energy levels of the Schrödinger equation and asymptotic behavior of the fundamental solution of the equation \(hu_ t=h^ 2\Delta u/2-V(x)u\)
• Splitting amplitudes of the lowest energy levels of the Schrödinger operator with double-well potential
• Tunneling and energy splitting in an asymmetric double-well potential
• Instantons, double wells and large deviations
• Multiple wells in the semi-classical limit I
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