Miloslav Znojil preprints

Miloslav Znojil: preprints

updated: December 17, 1999
contact data
CV data
with Czech version:
česká stránka
P A P E R S
1999


	SOLVABLE MODELS
*	Exact solution for Morse oscillator in PT-symmetric quantum mechanics Phys. Lett. A 264 (1999) 108-11
*	PT-symmetric harmonic oscillators Phys. Lett. A 259 (1999) 220-3

	PT SYMMETRIC QM
*	Hill-determinants and PT anharmonic oscillator J. Phys. A: Math. Gen. 32 (1999) 7419-28
*	Quasi-exact PT charged harmonic oscillator J. Phys. A: Math. Gen. 32 (1999) 4563
*	F. M. Fernández, R. Guardiola, J. Ros, M. Z., A family of complex potentials on the real line J. Phys. A: Math. Gen. 32 (1999) 3105, with

	DIRAC EQUATION
*	Quasi-riccatian solution method Mod. Phys. Lett. A 14 (1999) 863
*	Strongly singular models Phys. Lett. A 255 (1999) 1

	PERTURBATION THEORY
*	A new nonlinear formalism, quartic example J. Math. Chem., to appear

P L U S
talks


	CONFERENCES
*	Generalized Gauss functions Yerevan, June 29/July 4 1998
*	Non-diagonal unperturbed propagators Sydney, July 21/25 1997

	LECTURES
*	Paradoxes of PT symmetry - OTF NPI Rez (11 February 1999), - Doppler Institute Prague (23 February 1999), - MFF UK Prague (24 March 1999)

P L U S
the fresh texts of my
extended abstracts

	to be published in MATH. REVIEWS

*	30. 11. Hydrogen raising and lowering list.
*	17. 11. Arrow-Hurwitz algorithm is ``universal"
*	21. 10. Linear version of Calogero equation
*	15. 9. On a proof of convergence of finite elements
*	28. 7. On paper on special transformation brackets
*	15. 6. On paper on evaluation of self-energies
*	15. 6. Coulomb wave functions related to Heun equation
*	28. 5. Given the binding energy, they re-construct potentials!
*	28. 5. On a math. study of time-dependence of bound states
*	24. 5. Continued fractions reviewed
*	21. 4. Generalized eigenvalue problem: Fixing the norm of a resolvent on a vector one gets a ``pseudo-eigenvalue"
*	17. 3. Discretizing PDE
*	15. 2. Equal tractability of the bound and scattering (Coulomb) states
*	18. 1. The so called chiral oscillators

plus a few
O L D E R
papers on


	PERTURBATION THEORY
*	The strong-coupling expansions using PT symmetry F. M. Fernández, R. Guardiola, J. Ros and me, J. Phys. A: Math. Gen. 31 (1998) 10105
*	Perturbation expansions with Sturmians J. Math. Phys. 38 (1997) 5087
*	Hessenberg-matrix Hamiltonians Int. J. Mod. Phys. A 12 (1997) 299

	QUANTUM MECHANICS IN 2 DIMENSIONS
*	Asymptotically repulsive asymmetric confinement J. Phys. A: Math. Gen. 31 (1998) 3349
*	Shooting perturbation method in more dimensions J. Phys. A: Math. Gen. 30 (1997) 8771

	NUMERICAL METHODS
*	Quadrupled Schroedinger equation Phys. Lett. A 230 (1997) 283
*	Schroedinger equation de-discretized Phys. Lett. A 223 (1996) 411
*	Lanczos method for scattering Phys. Lett. A 211 (1996) 319

	RELATIVISTIC CORRECTIONS
*	Pauli-Schroedinger quasi-exact bound states J. Phys. A: Math. Gen. 29 (1996) 6443
*	Quasi-relativistic harmonic oscillators J. Phys. A: Math. Gen. 29 (1996) 2905

(returning to the

results once more?)

A short guide to preprints
deposited at LANL

Shape invariant potentials in PT symmetric quantum mechanics III.
(16. 12.: New solvable model: PT-regularized Poeschl-Teller. Real coupling constants, imaginary just shift of coordinates. Asymptotically vanishing singular example, possessing just the double set of strictly negative levels. Model with a nice duality feature. Submitted to
Phys. Rev. A.)

Shape invariant potentials in PT symmetric quantum mechanics II.
(7. 12.: New solvable model: PT-regularized Eckart. Asymptotically complex example, possessing a quasi-equidistant spectrum, positive and negative levels. Submitted to
Phys. Lett. A.)

Shape invariant potentials in PT symmetric quantum mechanics.
(29. 11.: New solvable model and paradox. Arbitrarily weak potential generates a bound state at an arbitrarily large energy. Submitted to
J. Phys. A.)

Triangular unperturbed propagators
(27. 10.: Innovated Rayleigh-Schroedinger perturbation theory. Applied to polynomial/polynomial anharmonicities. MS submitted to
J. Math. Chem.)

Generalized shape-invariant forces
(22. 9.: Method of solution using the innovated, matrix hypergeometric series. MS submitted to
J. Phys. A: Math. Gen.)

PT symmetric Morse oscillator
(31. 8.: An exactly solvable PT analogue of the double square well. MS submitted to Phys. Lett. A)

Beware boundary conditions!
(30. 9. 1998: showing that the famous Dutra's models (cf. Phys. Rev. A 47 (1993) R2435) are not exactly solvable)