6 citations · 20 across the 8 of their papers we have counts for
9 papers
SL(3,C) structure of one-dimensional Schrödinger equation
Toru Miyazawa
We present a new formalism for describing solutions of the one-dimensional stationary Schrödinger equation in terms of the Lie group SL(3,C) and its Lie algebra. In this formalism,…
Formulation of a unified method for low- and high-energy expansions in the analysis of reflection coefficients for one-dimensional Schrödinger equation
Toru Miyazawa
We study low-energy expansion and high-energy expansion of reflection coefficients for one-dimensional Schrödinger equation, from which expansions of the Green function can be obta…
To react or not to react? Intrinsic stochasticity of human control in virtual stick balancing
Arkady Zgonnikov, Ihor Lubashevsky, Shigeru Kanemoto +2
Understanding how humans control unstable systems is central to many research problems, with applications ranging from quiet standing to aircraft landing. Increasingly much evidenc…
Low-energy expansion formula for one-dimensional Fokker-Planck and Schrödinger equations with asymptotically periodic potentials
Toru Miyazawa
We consider one-dimensional Fokker-Planck and Schrödinger equations with a potential which approaches a periodic function at spatial infinity. We extend the low-energy expansion me…
Low-energy expansion formula for one-dimensional Fokker-Planck and Schrödinger equations with periodic potentials
Toru Miyazawa
We study the low-energy behavior of the Green function for one-dimensional Fokker-Planck and Schrödinger equations with periodic potentials. We derive a formula for the power serie…
Low-energy asymptotic expansion of the Green function for one-dimensional Fokker-Planck and Schrödinger equations
Toru Miyazawa
We consider Schrödinger equations and Fokker-Planck equations in one dimension, and study the low-energy asymptotic behavior of the Green function using a new method. In this metho…
High-energy asymptotic expansion of the Green function for one-dimensional Fokker-Planck and Schrödinger equations
Toru Miyazawa
A new formalism is presented for high-energy analysis of the Green function for Fokker-Planck and Schrödinger equations in one dimension. Formulas for the asymptotic expansion in p…
Analysis of reflection coefficients for the Fokker-Planck equation
Toru Miyazawa
Mathematical structure of the reflection coefficients for the one-dimensional Fokker-Planck equation is studied. A new formalism using differential operators is introduced and appl…
Expressions of the Green function in terms of reflection coefficients
Toru Miyazawa
We study the one-dimensional Schrödinger equation and derive exact expressions for the Green function in terms of reflection coefficients which are defined for semi-infinite interv…