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First, a misconception about the spectrum of a confined particle is evidentiated. Then, the results are shown to be incorrect by means of a counter-example, an explicit preparation for the probe is given that yields an arbitrary…

The weak measurement proposed by Aharonov and his colleagues extracts information of a physical quantity of the system by the post selection as the shifts of the argument of the probe wavefunction. The shift is called the weak value and is…

The variational perturbation theory for wave functions, which has been shown to work well for bound states of the anharmonic oscillator, is applied to resonance states of the anharmonic oscillator with negative coupling constant. We obtain…

Variational wave function ansatze are an invaluable tool to study the properties of strongly correlated systems. We propose such a wave function, based on the theory of auxiliary fields and combining aspects of auxiliary-field quantum Monte…

We show using statistically rigorous arguments that the technique of weak value amplification (WVA) does not perform better than standard statistical techniques for the tasks of single parameter estimation and signal detection. Specifically…

The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference,…

An exactly solvable time-dependent quantum mechanical problem is employed to study the convergence properties of transition amplitudes calculated by using the Schwinger variational principle. A detailed comparison between the amplitudes…

We give an exact formula for the Bellman function of the weak type of martingale transform. We also give the extremal functions (actually extremal sequences of functions). We find them using the precise form of the Bellman function. The…

Partial-wave analysis is one step in a process connecting experimental measurements to the N* states we are studying. Progress has been made in the area of `model-independent' analysis. However, more model-dependent approaches are needed to…

Weak measurement amplification, which is considered as a very promising scheme in precision measurement, has been applied to various small physical quantities estimation. Since many quantities can be converted to phase signal, it is thus…

We consider weakly coupled LQ optimal control problems and derive estimates on the sensitivity of the optimal value function in dependence of the coupling strength. In order to improve these sensitivity estimates a "coupling adapted" norm…

A new method is proposed to calculate wave functions in $k_T$-factorization in \cite{LiMi} as a comment about our paper \cite{FMW}. We point out that the results obtained with the method are in conflict with the translation invariance and…

We consider the functional inverse of the Gamma function in the complex plane, where it is multi-valued, and define a set of suitable branches by proposing a natural extension from the real case.

The weak measurements based amplification of ultra-small phase was proposed in our previous work. Due to the technical imperfections, the ability of amplification is usually limited in practice. Here we introduce the concept of cascaded…

The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…

Given a charge and current distribution with compact support, the associated potentials and fields are generally not integrable in the classical sense. However, it is convenient to be able to define their Fourier transform in order to…

Improving the phase resolution of interferometry is crucial for high-precision measurements of various physical quantities. Systematic phase errors dominate the phase uncertainties in most realistic optical interferometers. Here we propose…

The problem is addressed of defining the values of functions, whose variables tend to infinity, from the knowledge of these functions at asymptotically small variables close to zero. For this purpose, the extrapolation by means of different…

In this letter we investigate the common procedure in which any wave function is expanded into a series of eigenfunctions. It is shown that as far as dynamical systems are concerned the expanding procedure involves various mathematical and…

Based on the invariance of the phase of waves, plane waves was shown to propagate with negative frequencies in a medium which moves at superluminal speeds opposite to the propagation direction of plane waves. The validity of the invariance…