Related papers: The four postulates of quantum mechanics are three
The Hellmann-Feynman, virial and comparison theorems are three fundamental theorems of quantum mechanics. For the first two, counterparts exist for classical mechanics with relativistic or nonrelativistic kinetic energy. It is shown here…
Standard quantum theory represents a composite system at a given time by a joint state, but it does not prescribe a joint state for a composite of systems at different times. If a more even-handed treatment of space and time is possible,…
This work outlines a consistent method of identifying subsystems in finite-dimensional Hilbert spaces, independent of the underlying inner-product structure. Such Hilbert spaces arise in $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics,…
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…
In this paper we propose the idea that there is a corresponding relation between quantum states and points of the complex projective space, given that the number of dimensions of the Hilbert space is finite. We check this idea through…
In the past decades, quantum entanglement has been recognized to be the basic resource in quantum information theory. A fundamental need is then the understanding its qualification and its quantification: Is the quantum state entangled, and…
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…
In physics, experiments ultimately inform us as to what constitutes a good theoretical model of any physical concept: physical space should be no exception. The best picture of physical space in Newtonian physics is given by the…
The standard theory of quantum computation relies on the idea that the basic information quantity is represented by a superposition of elements of the canonical basis and the notion of probability naturally follows from the Born rule. In…
The classical Hilbert space formulation of the axioms of Quantum Mechanics appears to leave open the question whether the Hermitian operators which are associated with the observables of a finite non-relativistic quantum system are uniquely…
We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content…
We present an approach for teaching quantum physics at high school level based on the simplest quantum system - the single quantum bit (qubit). We show that many central concepts of quantum mechanics, including the superposition principle,…
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…
According to mathematical constructivism, a mathematical object can exist only if there is a way to compute (or "construct") it; so, what is non-computable is non-constructive. In the example of the quantum model, whose Fock states are…
A quantum set is defined to be simply a set of nonzero finite-dimensional Hilbert spaces. Together with binary relations, essentially the quantum relations of Weaver, quantum sets form a dagger compact category. Functions between quantum…
The state space of a homogeneous body is derived under two different assumptions: infinitesimal reducibility and irreducibility. The first assumption leads to a real vector space, used in classical mechanics, while the second one leads to a…
A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions…
Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start…
Quantum mechanics is a special kind of description of motion. The concept of wave function itself implies the openness of quantum system. We show that quantum mechanics describes the quantum correlation, i.e., entanglement, and information…
If the block universe view is correct, the future and the past have similar status and one would expect physical theories to involve final as well as initial boundary conditions. A plausible consistency condition between the initial and…