Modeling quantum harmonic oscillator in complex domain

DOI10.1016/j.chaos.2006.01.104zbMath1140.81371OpenAlexW1990709737MaRDI QIDQ927341

Ciann-Dong Yang

Publication date: 5 June 2008

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2006.01.104

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) Hamilton-Jacobi equations in mechanics (70H20)

Related Items (16)

Trajectory interpretation of correspondence principle: solution of nodal issue ⋮ Trajectory approach to the Schrödinger-Langevin equation with linear dissipation for ground states ⋮ Quantum Hamilton mechanics: Hamilton equations of quantum motion, origin of quantum operators, and proof of quantization axiom ⋮ Coherent states and modified de Broglie-Bohm complex quantum trajectories ⋮ Geometric phase within the complex quantum Hamilton-Jacobi formalism ⋮ Trajectory description of the quantum-classical transition for wave packet interference ⋮ Dissipative quantum trajectories in complex space: damped harmonic oscillator ⋮ Quantum Hamilton-Jacobi cosmology and classical-quantum correlation ⋮ Trajectory interpretation of the uncertainty principle in 1D systems using complex Bohmian mechanics ⋮ Arbitrary Lagrangian-Eulerian rate equation for the Born probability density in complex space ⋮ Strong chaos in one-dimensional quantum system ⋮ Complex tunneling dynamics ⋮ Quantum interference within the complex quantum Hamilton-Jacobi formalism ⋮ Parameterization of all path integral trajectories ⋮ Probability and complex quantum trajectories ⋮ A classical explanation of quantization

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hilbert, Fock and Cantorian spaces in the quantum two-slit gedanken experiment
• A PT-invariant potential with complex QES eigenvalues
• Nonlinear systems. Analysis, stability, and control
• \(\text{sl}(2, \mathbb C)\) as a complex Lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues
• Fractal black holes and information
• Algebraic and scattering aspects of a 𝒫𝒯-symmetric solvable potential
• Complex Extension of Quantum Mechanics
• Diffraction by volume gratings with imaginary potentials
• Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
• A newPT-symmetric complex Hamiltonian with a real spectrum
• Real and complex discrete eigenvalues in an exactly solvable one-dimensional complex PT-invariant potential
• Pseudo-Hermiticity of Hamiltonians under gauge-like transformation: real spectrum of non-Hermitian Hamiltonians

This page was built for publication: Modeling quantum harmonic oscillator in complex domain