@article{MTMT:33056353,
	title = {Determination of α – α interaction from experiment},
	url = {https://m2.mtmt.hu/api/publication/33056353},
	author = {Apagyi, Barnabás},
	doi = {10.1007/s10910-022-01382-3},
	journal-iso = {J MATH CHEM},
	journal = {JOURNAL OF MATHEMATICAL CHEMISTRY},
	volume = {60},
	unique-id = {33056353},
	issn = {0259-9791},
	abstract = {Fixed-energy quantum inversion method is applied to determine model independent alpha-particle scattering potentials within the energy range between 0 and 50 MeV. Only experimentally allowed even phase shifts are used in the calculation. Detailed results exhibited at low and higher energies show up a large interaction domain, a thin strong Pauli-blocking part and a smooth merging region between the colliding particles. Overall agreement between input and re-calculated phase shifts justifies the procedure.},
	keywords = {Newton method; Chemistry, Multidisciplinary; INVERSE-SCATTERING PROBLEM},
	year = {2022},
	eissn = {1572-8897},
	pages = {1739-1749}
}

@article{MTMT:2882736,
	title = {Quantum inversion with elastic phase shifts to discrete different energies},
	url = {https://m2.mtmt.hu/api/publication/2882736},
	author = {Scheid, W and Apagyi, Barnabás},
	doi = {10.1142/S0218301314500773},
	journal-iso = {INT J MOD PHYS E},
	journal = {INTERNATIONAL JOURNAL OF MODERN PHYSICS E-NUCLEAR PHYSICS},
	volume = {23},
	unique-id = {2882736},
	issn = {0218-3013},
	abstract = {We consider the inverse quantum scattering problem with phase shifts of different discrete energies belonging to a real energy-independent radial potential for elastic scattering. The solution of this problem is essential for atomic and nuclear physics. The two procedures investigated are based on the modified Newton-Sabatier method. The first procedure leads to angular-momentum dependent potentials with poles. The second one carries out an inversion at a fixed energy by varying the phase shifts of the other energies and leads finally to the correct energy-independent potential.},
	keywords = {FIXED ENERGY; SCATTERING PROBLEM; real potential; phase shifts to different discrete energies; Inverse quantum scattering problem},
	year = {2014},
	eissn = {1793-6608}
}

@article{MTMT:2696590,
	title = {The inverse scattering problem at fixed energy based on the Marchenko equation for an auxiliary Sturm-Liouville operator},
	url = {https://m2.mtmt.hu/api/publication/2696590},
	author = {Pálmai, Tamás Vencel and Apagyi, Barnabás},
	doi = {10.1088/1751-8113/46/4/045303},
	journal-iso = {J PHYS A-MATH THEOR},
	journal = {JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL},
	volume = {46},
	unique-id = {2696590},
	issn = {1751-8113},
	abstract = {A new approach is proposed to the solution of the quantum mechanical inverse scattering problem at a fixed energy. The method relates the fixed energy phase shifts to those arising in an auxiliary Sturm–Liouville problem via the interpolation theory of the Weyl–Titchmarsh m-function. Then a Marchenko equation is solved to obtain the potential. As an illustration test results are shown including the reconstructions of the piecewise constant and Coulomb-type potentials. A byproduct of the new framework is a demonstration of the connection found between the Gelfand–Levitan and Marchenko formalisms.},
	year = {2013},
	eissn = {1751-8121}
}

@article{MTMT:2284190,
	title = {Macroscopic quantum superpositon states of two-component Bose-Einstein condensates},
	url = {https://m2.mtmt.hu/api/publication/2284190},
	author = {Csire, Gábor and Apagyi, Barnabás},
	doi = {10.1103/PhysRevA.85.033613},
	journal-iso = {PHYS REV A},
	journal = {PHYSICAL REVIEW A},
	volume = {85},
	unique-id = {2284190},
	issn = {2469-9926},
	abstract = {We examine a two-component Bose-Einstein condensate in a double-well potential. We propose a model for the creation of many-particle macroscopic quantum superposition states. The effect of dissipation on the formation of these states is also investigated with the Monte Carlo wave-function technique. © 2012 American Physical Society.},
	keywords = {TRANSITION; EQUATION; Monte Carlo; Atoms; Monte Carlo methods; decoherence; ULTRACOLD GASES; VORTEX; Two-component; Bose-Einstein condensates; Macroscopic quantum; Double-well potential; Steam condensers},
	year = {2012},
	eissn = {2469-9934}
}

@article{MTMT:2688568,
	title = {Fixed energy potentials through an auxiliary inverse eigenvalue problem},
	url = {https://m2.mtmt.hu/api/publication/2688568},
	author = {Pálmai, Tamás Vencel and Apagyi, Barnabás},
	doi = {10.1088/0266-5611/28/8/085007},
	journal-iso = {INVERSE PROBL},
	journal = {INVERSE PROBLEMS},
	volume = {28},
	unique-id = {2688568},
	issn = {0266-5611},
	abstract = {An inverse scattering method based on an auxiliary inverse Sturm-Liouville problem recently proposed by Horvath and Apagyi (2008 Mod. Phys. Lett. B 22 2137) is examined in various aspects and developed further to (re) construct spherically symmetric fixed energy potentials of compact support realized in the three-dimensional Schrodinger equation. The method is generalized to obtain a family of inverse procedures characterized by two parameters originating, respectively, from the Liouville transformation and the solution of the inverse Sturm-Liouville problem. Both parameters affect the bound states arising in the auxiliary inverse spectral problem and one of them enables us to reduce their number which is assessed by a simple method. Various solution techniques of the underlying moment problem are proposed including the exact Cauchy matrix inversion method, usage of spurious bound state and assessment of the number of bound states. Examples include (re) productions of potentials from phase shifts known theoretically or derived from scattering experiments.},
	year = {2012},
	eissn = {1361-6420}
}

@article{MTMT:2680543,
	title = {Quantum Mechanical Inverse Scattering Problem at Fixed Energy: A Constructive Method},
	url = {https://m2.mtmt.hu/api/publication/2680543},
	author = {Pálmai, Tamás Vencel and Apagyi, Barnabás},
	doi = {10.4310/MAA.2011.v18.n1.a6},
	journal-iso = {METHODS APPL ANAL},
	journal = {METHODS AND APPLICATIONS OF ANALYSIS},
	volume = {18},
	unique-id = {2680543},
	issn = {1073-2772},
	year = {2011},
	eissn = {1945-0001},
	pages = {93-104}
}

@article{MTMT:2680538,
	title = {Interlacing of positive real zeros of Bessel functions},
	url = {https://m2.mtmt.hu/api/publication/2680538},
	author = {Pálmai, Tamás Vencel and Apagyi, Barnabás},
	doi = {10.1016/j.jmaa.2010.09.024},
	journal-iso = {J MATH ANAL APPL},
	journal = {JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS},
	volume = {375},
	unique-id = {2680538},
	issn = {0022-247X},
	year = {2011},
	eissn = {1096-0813},
	pages = {320-322}
}

@article{MTMT:2680753,
	title = {DISCUSSION OF QUANTUM INVERSE SCATTERING PROBLEMS FOR COUPLED CHANNELS AT FIXED ENERGY},
	url = {https://m2.mtmt.hu/api/publication/2680753},
	author = {Werner, Scheid and Apagyi, Barnabás},
	doi = {10.1142/S0218301311019660},
	journal-iso = {INT J MOD PHYS E},
	journal = {INTERNATIONAL JOURNAL OF MODERN PHYSICS E-NUCLEAR PHYSICS},
	volume = {20},
	unique-id = {2680753},
	issn = {0218-3013},
	year = {2011},
	eissn = {1793-6608},
	pages = {1765-1773}
}

@article{MTMT:2284192,
	title = {Effect of scattering lengths on the dynamics of a two-component Bose-Einstein condensate},
	url = {https://m2.mtmt.hu/api/publication/2284192},
	author = {Csire, Gábor and Schumayer, D and Apagyi, Barnabás},
	doi = {10.1103/PhysRevA.82.063608},
	journal-iso = {PHYS REV A},
	journal = {PHYSICAL REVIEW A},
	volume = {82},
	unique-id = {2284192},
	issn = {2469-9926},
	abstract = {We examine the effect of the intra- and interspecies scattering lengths on the dynamics of a two-component Bose-Einstein condensate, particularly focusing on the existence and stability of solitonic excitations. For each type of possible soliton pairs, stability ranges are presented in tabulated form. We also compare the numerically established stability of bright-bright, bright-dark, and dark-dark solitons with our analytical prediction and with that of Painlevé analysis of the dynamical equation. We demonstrate that tuning the interspecies scattering length away from the predicted value (keeping the intraspecies coupling fixed) breaks the stability of the soliton pairs. © 2010 The American Physical Society.},
	keywords = {SYSTEMS; STABILITY; SCATTERING; SOLITONS; PROPAGATION; Statistical mechanics; VORTEX; NONLINEAR SCHRODINGER-EQUATION; Two-component; Bose-Einstein condensates; Soliton pairs; Scattering length; Painleve; Existence and stability; Dynamical equation; Dark solitons; Analytical predictions; Steam condensers; PAINLEVE ANALYSIS},
	year = {2010},
	eissn = {2469-9934}
}

@article{MTMT:2657274,
	title = {Study of the Cox-Thompson inverse scattering method with a Coulomb potential},
	url = {https://m2.mtmt.hu/api/publication/2657274},
	author = {Hilk, D and Scheid, W and Pálmai, Tamás Vencel and Apagyi, Barnabás},
	doi = {10.1088/1751-8113/43/22/225302},
	journal-iso = {J PHYS A-MATH THEOR},
	journal = {JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL},
	volume = {43},
	unique-id = {2657274},
	issn = {1751-8113},
	abstract = {In order to learn more about the precision of the inversion by the Cox-Thompson method, we investigated the inversion of phase shifts of a singular potential, namely of a Coulomb potential. Using asymptotically Riccati-Bessel functions as reference functions, we could only approximately reproduce the singularity of the Coulomb potential at the origin. We also show uncertainties in the inverted potential due to different minima in the minimization solution of the nonlinear equations of the Cox-Thompson procedure. As a result, we conclude that one has to take much care with the inversion of experimental phase shifts suffering from measurement errors.},
	year = {2010},
	eissn = {1751-8121}
}

@article{MTMT:2657276,
	title = {Development of a Cox-Thompson inverse scattering method to charged particles},
	url = {https://m2.mtmt.hu/api/publication/2657276},
	author = {Pálmai, Tamás Vencel and Apagyi, Barnabás and Scheid, W},
	doi = {10.1088/0954-3899/37/2/025101},
	journal-iso = {J PHYS G NUCL PARTIC},
	journal = {JOURNAL OF PHYSICS G-NUCLEAR AND PARTICLE PHYSICS},
	volume = {37},
	unique-id = {2657276},
	issn = {0954-3899},
	abstract = {A Cox-Thompson fixed-energy quantum inverse scattering method is developed further to treat long-range Coulomb interaction. Depending on the reference potentials chosen, two methods have been formulated which produce inverse potentials with singular or finite value at the origin. Based on the quality of reproduction of input experimental phase shifts, it is guessed that the p-a interaction possesses an interesting repulsive hard core.},
	year = {2010},
	eissn = {1361-6471}
}

@article{MTMT:2657275,
	title = {On nonsingular potentials of Cox-Thompson inversion scheme},
	url = {https://m2.mtmt.hu/api/publication/2657275},
	author = {Pálmai, Tamás Vencel and Apagyi, Barnabás},
	doi = {10.1063/1.3282849},
	journal-iso = {J MATH PHYS},
	journal = {JOURNAL OF MATHEMATICAL PHYSICS},
	volume = {51},
	unique-id = {2657275},
	issn = {0022-2488},
	abstract = {We establish a condition for obtaining nonsingular potentials using the Cox-Thompson inverse scattering method with one phase shift. The anomalous singularities of the potentials are avoided by maintaining unique solutions of the underlying Regge-Newton integral equation for the transformation kernel. As a by-product, new inequality sequences of zeros of Bessel functions are discovered. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3282849]},
	year = {2010},
	eissn = {1089-7658}
}

@article{MTMT:2657280,
	title = {QUANTUM INVERSE SCATTERING PROBLEM FOR COUPLED CHANNELS},
	url = {https://m2.mtmt.hu/api/publication/2657280},
	author = {Apagyi, Barnabás and Scheid, W},
	doi = {10.1142/S021798490801700X},
	journal-iso = {MOD PHYS LETT B},
	journal = {MODERN PHYSICS LETTERS B},
	volume = {22},
	unique-id = {2657280},
	issn = {0217-9849},
	abstract = {The article gives a concise review on methods for solving the inverse scattering problem of coupled reaction channels in quantum mechanics at fixed energy and presents specific applications to nuclear reactions. Two methods are considered, namely the Newton Sabatier method and an approximate method based on the first Born approximation. Examples with artificial coupling potentials are shown to provide successful tests of both the methods. Further developments of the coupled channel inverse problem at fixed energy are needed for manifold applications in various fields of physics.},
	year = {2008},
	eissn = {1793-6640},
	pages = {2241-2256}
}

@article{MTMT:2657277,
	title = {Proceedings of the International Conference on Inverse Quantum Scattering Theory, 27-31 August 2007, Siofok, Hungary PREFACE},
	url = {https://m2.mtmt.hu/api/publication/2657277},
	author = {Apagyi, Barnabás and Horváth, Miklós},
	journal-iso = {MOD PHYS LETT B},
	journal = {MODERN PHYSICS LETTERS B},
	volume = {22},
	unique-id = {2657277},
	issn = {0217-9849},
	year = {2008},
	eissn = {1793-6640},
	pages = {V-V}
}

@misc{MTMT:2664372,
	title = {Proceedings of the International Conference on Inverse Quantum Scattering Theory},
	url = {https://m2.mtmt.hu/api/publication/2664372},
	editor = {Apagyi, Barnabás and Horváth, Miklós},
	publisher = {World Scientific Publishing Co. Pte. Ltd.},
	unique-id = {2664372},
	year = {2008}
}

@article{MTMT:2657278,
	title = {Solution of the inverse scattering problem at fixed energy for potentials being zero beyond a fixed radius},
	url = {https://m2.mtmt.hu/api/publication/2657278},
	author = {Horváth, Miklós and Apagyi, Barnabás},
	doi = {10.1142/S0217984908016923},
	journal-iso = {MOD PHYS LETT B},
	journal = {MODERN PHYSICS LETTERS B},
	volume = {22},
	unique-id = {2657278},
	issn = {0217-9849},
	abstract = {Based on the relation between the m-function and the spectral function we construct an inverse quantum scattering procedure at fixed energy which can be applied to spherical radial potentials vanishing beyond a fixed radius alpha. To solve the Gelfand-Levitan-Marchenko integral equation for the transformation kernel, we determine the input symmetrical kernel by using a minimum norm method with moments defined by the input set of scattering phase shifts. The method applied to the box and Gauss potentials needs further practical developments regarding the treatment of bound states.},
	year = {2008},
	eissn = {1793-6640},
	pages = {2137-2149}
}

@article{MTMT:2657282,
	title = {Simplified solutions of the Cox-Thompson inverse scattering method at fixed energy},
	url = {https://m2.mtmt.hu/api/publication/2657282},
	author = {Pálmai, Tamás Vencel and Horváth, Miklós and Apagyi, Barnabás},
	doi = {10.1088/1751-8113/41/23/235305},
	journal-iso = {J PHYS A-MATH THEOR},
	journal = {JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL},
	volume = {41},
	unique-id = {2657282},
	issn = {1751-8113},
	abstract = {Simplified solutions of the Cox-Thompson inverse quantum scattering method at fixed energy are derived if a finite number of partial waves with only even or odd angular momenta contribute to the scattering process. Based on new formulae various approximate methods are introduced which also prove applicable to the generic scattering events.},
	year = {2008},
	eissn = {1751-8121}
}

@article{MTMT:2657279,
	title = {SEMI-ANALYTIC EQUATIONS TO THE COX-THOMPSON INVERSE SCATTERING METHOD AT FIXED ENERGY FOR SPECIAL CASES},
	url = {https://m2.mtmt.hu/api/publication/2657279},
	author = {Pálmai, Tamás Vencel and Horváth, Miklós and Apagyi, Barnabás},
	doi = {10.1142/S0217984908016972},
	journal-iso = {MOD PHYS LETT B},
	journal = {MODERN PHYSICS LETTERS B},
	volume = {22},
	unique-id = {2657279},
	issn = {0217-9849},
	abstract = {Solution of the Cox-Thompson inverse scattering problem at fixed energy(1-3) is reformulated resulting in semi-analytic equations. The new set of equations for the normalization constants and the nonphysical (shifted) angular momenta are free of matrix inversion operations. This simplification is a result of treating only the input phase shifts of partial waves of a given parity. Therefore, the proposed method can be applied for identical particle scattering of the bosonic type (or for certain cases of identical fermionic scattering). The new formulae are expected to be numerically more efficient than the previous ones. Based on the semi-analytic equations an approximate method is proposed for the generic inverse scattering problem, when partial waves of arbitrary parity are considered.},
	year = {2008},
	eissn = {1793-6640},
	pages = {2191-2199}
}

@article{MTMT:2657283,
	title = {Effective Rb-Rb inter-atomic potential from ultracold Bose-gas collisions},
	url = {https://m2.mtmt.hu/api/publication/2657283},
	author = {Schumayer, D and Melchert, O and Scheid, W and Apagyi, Barnabás},
	doi = {10.1088/0953-4075/41/3/035302},
	journal-iso = {J PHYS B AT MOL OPT PH},
	journal = {JOURNAL OF PHYSICS B: ATOMIC MOLECULAR AND OPTICAL PHYSICS},
	volume = {41},
	unique-id = {2657283},
	issn = {0953-4075},
	abstract = {Scattering phase shifts obtained from Rb-87 Bose-gas collision experiments are used to reconstruct effective potentials resulting, self-consistently, in the same scattering events observed in the experiments at a particular energy. We have found that the interaction strength close to the origin suddenly changes from repulsion to attraction when the collision energy crosses, from below, the l = 2 shape resonance position at E approximate to 275 mu K. This observation may be utilized in outlining future Bose-gas collision experiments.},
	year = {2008},
	eissn = {1361-6455}
}

@article{MTMT:2657281,
	title = {Phase estimation procedure to solve quantum-mechanical eigenvalue problems},
	url = {https://m2.mtmt.hu/api/publication/2657281},
	author = {Varga, P and Apagyi, Barnabás},
	doi = {10.1103/PhysRevA.78.022337},
	journal-iso = {PHYS REV A},
	journal = {PHYSICAL REVIEW A},
	volume = {78},
	unique-id = {2657281},
	issn = {2469-9926},
	abstract = {A simple phase estimation procedure is outlined and applied to solve standard quantum-mechanical problems. The procedure needs only one qubit to read off the eigenenergy obtained by iterative measurements, while the system qubits provides the corresponding eigenstates. No a priori information is needed about the system states and energies, therefore, the procedure may be launched from a completely random initial state.},
	year = {2008},
	eissn = {2469-9934}
}