Related papers: Many-Worlds and Schroedinger's First Quantum Theor…
The assumptions added by Bohr and concerning the Hilbert space (formed by all solutions of Schroedinger equation) changed fundamentally the original physical interpretation of these solutions proposed earlier by Schroedinger. This new…
I argue that the many worlds explanation of quantum computation is not licensed by, and in fact is conceptually inferior to, the many worlds interpretation of quantum mechanics from which it is derived. I argue that the many worlds…
The full spectrum and eigenfunctions of the quantum version of a nonlinear oscillator defined on an N-dimensional space with nonconstant curvature are rigorously found. Since the underlying curved space generates a position-dependent…
This paper deals with the foundations of quantum mechanics. We start by outlining the characterisation, due to Birkhoff and Von Neumann, of the logical structures of the theories of classical physics and quantum mechanics, as boolean and…
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…
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…
The challenges posed by the development of field theories, both classical and quantum, force us to question their most basic and foundational ideas like the role and origin of space-time, the meaning of physical states, etc. Among them the…
When quantum mechanics was developed in the '20s of the last century another revolution in physics was just starting. It began with the discovery that the universe is expanding. For a long time quantum mechanics and cosmology developed…
In classical physics, there is a basic principle, namely "A particle cannot be located at the position of another one on the same time". Which consequences can be derived if this principle is transferred into quantum physics? For doing…
The measurement problem in quantum mechanics originates in the inability of the Schr\"odinger equation to predict definite outcomes of measurements. This is due to the lack of objectivity of the eigenstates of the measuring apparatus. Such…
The functional Schr\"odinger equation in curved space-time is derived from the manifestly covariant precanonical Schr\"odinger equation. The Schr\"odinger wave functional is expressed as the trace of the multidimensional product integral of…
This paper is an answer to the first part of Adrian Kent's One World versus Many : the Inadequacy of Everettian Accounts of Evolution, Probability, and Scientific Confirmation [arXiv:0905.0624]. We take issue with Kent's arguments against…
This paper provides a detailed historical account of early debates over wave-function realism, the modern term for the view that the wave function of quantum theory is physically real. As this paper will show, the idea of physical waves…
In his seminal part IV, Ann. der Phys. Vol 81, 1926 paper, Schrodinger has developed a clear understanding about the wave equation that produces the correct quadratic dispersion relation for matter-waves and he first presents a real-valued…
It is first shown that when the Schr\"{o}dinger equation for a wave function is written in the polar form, complete information about the system's {\em quantum-ness} is separated out in a single term $Q$, the so called `quantum potential'.…
We prove a theorem showing that quantum mechanics is not directly a stochastic process characterizing Brownian motion but rather its square root. This implies that a complex-valued stochastic process is involved. Schr\"odinger equation is…
In the present paper, in terms of the measurability concept introduced in the previous works of the author, a quantum theory is studied. Within the framework of this concept, several examples are considered using the Schrodinger picture;…
In the present paper, the decision problem of the Schr\"odinger equation (asking whether or not a given Hamiltonian operator has the nonempty solution set) is represented as a logical statement. As it is shown in the paper, the law of…
Many worlds interpretations (MWI) of quantum mechanics avoid the measurement problem by considering every term in the quantum superposition as actual. A seemingly opposed solution is proposed by modal interpretations (MI) which state that…
The classical limit $\hbar$->0 of quantum mechanics is known to be delicate, in particular there seems to be no simple derivation of the classical Hamilton equation, starting from the Schr\"odinger equation. In this paper I elaborate on an…