Related papers: The Physical Origin of Schr\"odinger Equation
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schr\"odinger equation, which is solved for the wave function, bound…
The dynamics of any classical-mechanics system can be formulated in the reparametrization-invariant (RI) form (that is we use the parametric representation for trajectories, ${\bf x}={\bf x}(\tau)$, $t=t(\tau)$ instead of ${\bf x}={\bf…
Starting from our idea of combining the Feynman path integral spirit and the Dyson series kernel, we find an explicit and general form of time evolution operator that is a $c$-number function and a power series of perturbation including all…
Bohmian mechnaics is the most naively obvious embedding imaginable of Schr\"odingers's equation into a completely coherent physical theory. It describes a world in which particles move in a highly non-Newtonian sort of way, one which may at…
New insight to the principles of the quantum physics development is given. The correct ways for the construction of new versions of quantum mechanics on the second main postulate base are discussed. The conclusion on the status of the…
We consider the special and general relativistic extensions of the action principle behind the Schr\"odinger equation distinguishing classical and quantum contributions. Postulating a particular quantum correction to the source term in the…
It is well known that the Schr\"odinger equation is only suitable for the particle in common potential $V(\vec{r},t)$. In this paper, a general Quantum Mechanics is proposed, where the Lagrangian is the general form. The new quantum wave…
Any time-dependent solution of Schr\"{o}dinger equation may be always correlated to a solution of Hamilton equations or to a statistical combination of their solutions; only the set of corresponding solutions is somewhat smaller (due to…
Within the framework of self-adjoint operator of time in non-relativistic quantum mechanics the equation describing change of the state of quantum system with respect to energy is introduced. The operator of time appears to be the generator…
Quantum mechanics is derived as an application of the method of maximum entropy. No appeal is made to any underlying classical action principle whether deterministic or stochastic. Instead, the basic assumption is that in addition to the…
The introduction of nonlinearities in the Schr\"odinger equation has been considered in the literature as an effective manner to describe the action of external environments or mean fields. Here, in particular, we explore the nonlinear…
A general theory is presented of quantum mechanics of singular, non-autonomous, higher derivative systems. Within that general theory, $n$-th order and $m$-th order Lagrangians are shown to be quantum mechanically equivalent if their…
A quaternionic version of Quantum Mechanics is constructed using the Schwinger's formulation based on measurements and a Variational Principle. Commutation relations and evolution equations are provided, and the results are compared with…
The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show Using no physical hypotheses) that the Schroedinger equation for a nonrelativistic system of spinless…
A new picture of Quantum Mechanics based on the theory of groupoids is presented. This picture provides the mathematical background for Schwinger's algebra of selective measurements and helps to understand its scope and eventual…
Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such…
The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical…
A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's…
In their constructions of system of quantum stochastic differential equations, mathematicians and/or several physicists interpret that the function of random force operator is to preserve the canonical commutation relation in time, i.e., to…
The present contribution is based on the assumption that the probabilistic character of quantum mechanics does not originate from uncertainties caused by the process of measurement or observation, but rather reflects the presence of…