Bohr-Sommerfeld quantization condition for Dirac states derived from an Ermakov-type invariant

DOI10.1063/1.4803030zbMath1282.81084OpenAlexW2025232530MaRDI QIDQ5402278

Patrick McCabe, Karl-Erik Thylwe

Publication date: 6 March 2014

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.4803030

Mathematics Subject Classification ID

Nuclear physics (81V35) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Atomic physics (81V45) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

Cites Work

• Non-oscillating solutions to uncoupled Ermakov systems and the semi-classical limit
• Amplitude-phase calculations of Regge poles obtained from coupled radial Dirac equations
• Application of the exact quantization rule to the relativistic solution of the rotational Morse potential with pseudospin symmetry
• Amplitude-phase methods for analyzing the radial Dirac equation: calculation of scattering phase shifts
• The damped Pinney equation and its applications to dissipative quantum mechanics
• A direct approach to finding exact invariants for one-dimensional time-dependent classical Hamiltonians
• A Note on the Time-Dependent Harmonic Oscillator
• On a Generalization of the Lewis Invariant for the Time-Dependent Harmonic Oscillator
• The algebraic structure of generalized Ermakov systems in three dimensions
• Note on invariants for uncoupled Ermakov systems
• The barrier transmission problem treated by the amplitude-phase method and expressed in terms of an invariant of the Ermakov–Lewis type
• ScatteringS-matrix derived from invariants of the Ermakov–Lewis type
• Semiclassical aspects and supersymmetry of bound Dirac states for central pseudo-scalar potentials
• On Regge pole trajectories for a rational function approximation of Thomas–Fermi potentials
• Exact Quantization Conditions. II
• Coupled radial Schrödinger equations written as Dirac-type equations: application to an amplitude-phase approach
• The nonlinear differential equation 𝑦”+𝑝(𝑥)𝑦+𝑐𝑦⁻³=0

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