Neutrino Oscillations and Time-Energy Uncertainty Relation

Neutrino oscillations is a phenomenon which is characterized by a finite oscillation time (length). For such phenomena time-energy uncertainty relation is valid. This means that energy uncertainty is needed for oscillations to occur. We consider neutrino oscillations from this point of view. We demonstrate that for mixed neutrino states, which describe flavor neutrinos $\nu_{e}$, $\nu_{\mu}$ and $\nu_{\tau}$, translational invariance does not take place.Comment: 14 page

The Three-Neutrino Mixing and Oscillations

The basics of neutrino oscillations is presented. Existing evidences of neutrino oscillations, obtained in the atmospheric and solar neutrino experiments, are considered. The new CHOOZ bound on the element $|U_{e3}|^{2}$, obtained from the three-neutrino analysis of the data, is discussed. Decoupling of neutrino oscillations in the solar neutrino range of $\Delta m^{2}$ is considered.Comment: Lectures at Corfu Summer Institute on Elementary Particle Physics, Corfu, 31.8 - 20.9. 200

Early years of neutrino oscillations

The first papers on neutrino oscillations are shortly reviewed.Comment: 10 page

The History of Neutrino Oscillations

The early history of neutrino masses, mixing and oscillations is briefly reviewed.Comment: A report at the ``Nobel Symposium on Neutrino physics'', Haga Slott, Enkoping, Sweden, August 19-24, 200

Neutrino masses and oscillations

A report on neutrino masses, mixing and oscillations, made in Dubna at the symposium dedicated to 100 years of the Rutherford's discovery of atomic nucleus, is presented. We start with the hypothesis of neutrino which was proposed by W. Pauli in December 1930 in order to solve some problems of nuclei (the problem of spin of $^{7}N_{14}$ and other nuclei and the problem of continuous $\beta$-spectra). After that we consider the theory of massless two-component neutrino and first ideas of neutrino oscillations which were put forward by B. Pontecorvo in Dubna in 1957-58. The present status of neutrino mixing and oscillations is briefly reviewed. The seesaw mechanism of the generation of small Majorana neutrino masses is discussed and neutrinoless double $\beta$-decay of nuclei is considered. A possibility to probe the Majorana mass mechanism of the $0\nu\beta\beta$-decay is discussed.Comment: A report at the symposium "100th anniversary of the discovery of atomic nucleus" March 10-11, 2011, JINR, Dubna, Russi

Neutrino Mixing

In the first part of these lectures the neutrino mixing hypothesis will be considered in detail. We will discuss the possible schemes of neutrino mixing and present the data of the recent experiments searching for effects due to nonvanishing neutrino masses and mixing angles.In the second part of these lectures the physics of solar neutrinos will be considered.We will discuss the MSW resonance solution of the equation of evolution of a neutrino in matter and present data of solar neutrino experiments.Comment: DFTT 67/92, LaTeX file, no figure

Recoilless Resonance Absorption of Tritium Antineutrinos and Time-Energy Uncertainty Relation

We discuss neutrino oscillations in an experiment with M\"ossbauer recoilless resonance absorbtion of tritium antineutrinos, proposed recently by Raghavan. We demonstrate that small energy uncertainty of antineutrinos which ensures a large resonance absorption cross section is in a conflict with the energy uncertainty which, according to the time-energy uncertainty relation, is necessary for neutrino oscillations to happen. The search for neutrino oscillations in the M\"ossbauer neutrino experiment would be an important test of the applicability of the time-energy uncertainty relation to a newly discovered interference phenomenon

On the phenomenology of neutrino oscillations in vacuum

A simple method of the calculation of neutrino transition probabilities in vacuum in the general case of $n$ massive neutrinos is presented. The method proposed fully utilizes the unitarity of the mixing matrix. Three-neutrino case for both neutrino mass hierarchies is considered in some details. Transitions in the case of the sterile neutrinos are also discussed

A Remark on Neutrino Oscillations and Time-Energy Uncertainty Relation

Neutrino oscillations are discussed from the point of view of the time-energy uncertainty relation

A Lecture on Neutrinos

The major steps in the development of our knowledge about neutrinos are reviewed. The basics of neutrino oscillation formalism is presented. Neutrino oscillations in the framework of three-neutrino mixing are considered. The evidence for neutrino oscillations is discussed