Related papers: Hamiltonian Formalism in Quantum Mechanics
The main result of this note is a characterization of the Poisson commutativity of Hamilton functions in terms of their principal action functions.
Classical and quantum physics represent two distinct theories; however, quantum physics is regarded as the more fundamental of the two. It is posited that classical mechanics should arise from quantum mechanics under certain limiting…
Several quantum gravity and string theory thought experiments indicate that the Heisenberg uncertainty relations get modified at the Planck scale so that a minimal length do arises. This modification may imply a modification of the…
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…
Connecting ideas of geometric formulation of quantum mechanics with new results in symplectic geometry a new approach to geometrical quantization procedure is proposed. As a first result we verify that the correspondence between "classical"…
The dynamic of a classical system can be expressed by means of Poisson brackets. In this paper we generalize the relation between the usual non covariant Hamiltonian and the Poisson brackets to a covariant Hamiltonian and new brackets in…
Bosonic quantum conversion systems can be modeled by many-particle single-mode Hamiltonians describing a conversion of $n$ molecules of type A into $m$ molecules of type B and vice versa. These Hamiltonians are analyzed in terms of…
The formulation of classical mechanics applicable to fermionic degrees of freedom is presented in mathematically rigorous terms, including a description of how the mathematical structure relates to the quantization of the theory. Canonical…
Starting from a simple classical framework and employing some stochastic concepts, the basic ingredients of the quantum formalism are recovered. It has been shown that the traditional axiomatic structure of quantum mechanics can be rebuilt,…
We review here the quantum mechanics of some noncommutative theories in which no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. We show how the difference of structure between the Poisson brackets and…
It is shown that quantum mechanics on noncommutative spaces (NQM) can be obtained by the canonical quantization of some underlying second class constrained system formulated in extended configuration space. It leads, in particular, to an…
Quantum mechanics of models is considered which are constructed in spaces with Lie algebra type commutation relations between spatial coordinates. The case is specialized to that of the group SU(2), for which the formulation of the problem…
It is shown that q-deformed quantum mechanics (systems with q-deformed Heisenberg commutation relations) can be interpreted as an ordinary quantum mechanics on Kaehler manifolds, or as a quantum theory with second (or first)- class…
Five physical assumptions are proposed that together entail the general qualitative results, including the Born rule, of non-relativistic quantum mechanics by physical and information-theoretic reasoning alone. Two of these assumptions…
Biconformal spaces contain the essential elements of quantum mechanics, making the independent imposition of quantization unnecessary. Based on three postulates characterizing motion and measurement in biconformal geometry, we derive…
We discuss in this paper the canonical structure of classical field theory in finite dimensions within the {\it{pataplectic}} hamiltonian formulation, where we put forward the role of Legendre correspondance. We define the Poisson…
In this work, the commutator of any two reasonable functions of several pairs of canonical conjugate operators is obtained as a sum of terms of partial derivatives of those functions (equations 9, 10 or 11). When applied to quantum…
For the symmetric harmonic oscillator and the symmetric bouncer defined in 2-D, two different Hamiltonian are given describing the same classical dynamics; however, their quantum dynamics behavior are different.
For some time the York time parameter has been identified as a candidate for a physically meaningful time in cosmology. An associated Hamiltonian may be found by solving the Hamiltonian constraint for the momentum conjugate to the York time…
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this…