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Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…

We first recall a fact which is well-known among mathematical physicists although lesser-known among theoretical physicists that the standard quantum mechanics over a complex Hilbert space, is a Hamiltonian mechanics, regarding the Hilbert…

The article suggests that quantum mechanics is a science of a new type, which refutes the classical metaphysical concept of reality. The notion of a quantum concept is introduced. The possibility of a Wittgensteinian 'dissolution' of the…

A real two-particle experiment is proposed in which one of the particles undergoes two successive impacts on beam-splitters. It is shown that the standard quantum mechanical superposition principle implies the possibility of influences…

Relevant algebraic structures for the description of Quantum Mechanics in the Heisenberg picture are replaced by tensorfields on the space of states. This replacement introduces a differential geometric point of view which allows for a…

The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…

The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding…

One of the most significant debates of our time is whether our macroscopic world (i) naturally emerges from quantum mechanics or (ii) requires new physics. We argue for the latter and propose a simple gravitational self-decoherence…

The quantum mechanical commutation relations, which are directly related to the Heisenberg uncertainty principle, have a crucial importance for understanding the quantum mechanics of students. During undergraduate level courses, the…

Some predictions of quantum mechanics are in contrast with the macroscopic realm of everyday experience, in particular those originated by the Heisenberg uncertainty principle, encoded in the non-commutativity of some measurable operators.…

A modified form of quantum mechanics which includes a new mechanism for wavefunction collapse is proposed. The collapse provides a solution to the quantum measurement problem. This modified quantum mechanics is shown to arise naturally from…

Theory of scattering of a quantum-mechanical particle on a cosmic string is developed. S-matrix and scattering amplitude are determined as functions of the flux and the tension of the string. We reveal that, in the case of the nonvanishing…

In this article we discuss the contextual character of quantum mechanics in the framework of modal interpretations. We investigate its historical origin and relate contemporary modal interpretations to those proposed by M. Born and W.…

We present a quantum kinetic theory for spin-$1/2$ particles, including the spin-orbit interaction, retaining particle dispersive effects to all orders in $\hbar$, based on a gauge-invariant Wigner transformation. Compared to previous…

A version of quantum theory is derived from a set of plausible assumptions related to the following general setting: For a given system there is a set of experiments that can be performed, and for each such experiment an ordinary…

Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…

We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…

Quantum entanglement and relativistic causality are key concepts in theoretical works seeking to unify quantum mechanics and gravity. In this article, we show that the interplay between relativity theory and quantum entanglement has…

The quantization of a single particle without spin in an appropriate curved space-time is considered. The Hamilton formalism on reduced space for a particle in a curved space-time is constructed and the main aspects of quantization scheme…

Quantum mechanical interference of wave functions leads to some difficulties if a probability density is considered as a source of gravity. We show that an introduction of a quantum energy-momentum tensor as a source term in Einstein…