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Guessing Quantum States from Images of their Zeros in the Complex Plane

Janowicz Maciej, Zembrzuski Andrzej

Machine Graphics and Vision

2023

Vol. 32, No. 3/4

147--159

The problem of determining the wave function of a physical system based on the graphical representation of its zeros is considered. It can be dealt with by invoking the Bargmann representation in which the wave functions are represented by analytic functions with an appropriate definition of the scalar product. The Weierstrass factorization theorem can then be applied. Examples of states that can be guessed from the pictorial representation of zeros by both the human eye and, possibly, by machine learning systems are given. The quality of recognition by the latter has been tested using Convolutional Neural Networks.

Interpolations of Bargmann type measures

Asai N., Krystek A. D., Wojakowski Ł. J.

Demonstratio Mathematica

2016

Vol. 49, nr 3

293--301

In this paper, we shall discuss Bargmann type measures on C for several classes of probability measures on R. The unified interpolation expressions include not only the classical Bargmann measure and its q-deformation, but also their t-deformations and dilations. As a special case, we get conditions on existence and an explicit form of the Bargmann representation for the free Meixner family of probability measures.

Bargmann measures for t-deformed probability

Krystek A. D., Wojakowski Ł. J.

Probability and Mathematical Statistics

2014

Vol. 34, Fasc. 2

279--291

It is shown that the Bargmann representation of a t-deformed probability measure can be obtained by taking away some t-dependent amount of mass at zero of the Bargmann representation of the original measure and scaling of the remaining part. This allows us to formulate conditions on existence of the Bargmann representation of a t-deformed probability measure and to study some prominent examples.