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A method is presented to compute approximate solutions for eigenequations in quantum mechanics with an arbitrary kinetic part. In some cases, the approximate eigenvalues can be analytically determined and they can be lower or upper bounds.…
We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under…
An infinite sequence of potential well functions is considered. A trial wavefunction is used with the Schr$\ddot{\text{o}}$dinger equation to obtain an approximate ground state energy for each potential well function. We obtain an…
The main fundamental principles characterizing the vacuum field structure are formulated, the modeling of the related vacuum medium and charged point particle dynamics by means of devised field theoretic tools are analyzed. The Maxwell…
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…
It is shown that, in some cases, the effect of discrete distributions of flux lines in quantum mechanics can be associated with the effect of continuous distributions of magnetic fields with special symmetries. In particular, flux lines…
A persistent focus on the concept of emergence as a core element of the scientific method allows a clean separation, insofar as this is possible, of the physical and philosophical aspects of the problem of outcomes in quantum mechanics. The…
We obtain the exact energy spectrum of nonuniform mass particles for a collection of Hamiltonians in a three-dimensional approach to a quantum dot. By considering a set of generalized Schr\"odinger equations with different orderings between…
Geometric (Schrodinger) quantization of nonrelativistic mechanics with respect to different reference frames is considered. In classical nonrelativistic mechanics, a reference frame is represented by a connection on a configuration space…
It is known that solutions of Richardson equations can be represented as stationary points of the "energy" of classical free charges on the plane. We suggest to consider "probabilities" of the system of charges to occupy certain states in…
A basic aspect of the recently proposed approach to quantum mechanics is that no use of any axiomatic interpretation of the wave function is made. In particular, the quantum potential turns out to be an intrinsic potential energy of the…
The classical energy conditions are known to not be fundamental physics -- they are typically violated by semiclassical quantum effects. Consequently, some effort has gone into finding possible semiclassical replacements for the classical…
We argue that statistical mechanics of systems with relaxation implies breaking the energy function of systems into two having different transformation rules. With this duality the energy approach incorporates the generalized vortex forces.…
A goal of physics is to understand the greatest possible breadth of natural phenomena in terms of the most economical set of basic concepts. However, as the understanding of physics has developed historically, its pedagogy and language have…
We define the state of minimum energy while the expectation values of the field operators and their time derivatives in a determined moment in such a state are constrained. As an axiom, we consider such a state as the background of the…
Quantum mechanics has about a dozen exactly solvable potentials. Normally, the time-independent Schroedinger equation for them is solved by using a generalized series solution for the bound states (using the Froebenius method) and then an…
We have previously presented a version of the Weak Equivalence Principle for a quantum particle as an exact analog of the classical case, based on the Heisenberg picture analysis of free particle motion. Here, we take that to a full…
In quantum field theory there is now a well developed technique, effective field theory, which allows one to obtain low energy quantum predictions in ``non-renormalizable'' theories, using only the degrees of freedom and interactions…
Finding the ground state of a quantum mechanical system can be formulated as an optimal control problem. In this formulation, the drift of the optimally controlled process is chosen to match the distribution of paths in the Feynman--Kac…
Based on a number of experimentally verified physical observations, it is argued that the standard principles of quantum mechanics should be applied to the Universe as a whole. Thus, a paradigm is proposed in which the entire Universe is…