Related papers: Schrodinger Equation cannot Describe Transition Pr…
An important class of resonance problems involves the study of perturbations of systems having embedded eigenvalues in their continuous spectrum. Problems with this mathematical structure arise in the study of many physical systems, e.g.…
A method of solving the time-dependent Schr\"odinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wave-functions on to the rest of the system replaced by an…
Within Bohm`s interpretation of quantum mechanics particles follow classical trajectories that are determined by the full solution of the time dependent Schroedinger equation. If this interpretation is consistent it must be possible to…
We show that the emergence of time evolution in an otherwise timeless nonrelativistic closed quantum system -- viewed as a poor man's model of generally covariant quantum theory -- can be understood from the perspective of the path integral…
In non-relativistic quantum mechanics, path integrals are normally derived from the Schroedinger equation. This assumes the two formalisms are equivalent. Since time plays a very different role in the Schroedinger equation and in path…
The difficulty that the probabilities infinitely increase with time as time is long enough in time-dependent perturbation theory for some quantum systems is resolved by means of simply transforming the perturbative series into natural…
Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…
In quantum physics, disturbance due to a measurement is not negligible. This requires the time parameter $t$ in the Schr\"odinger or Heisenberg equation to be considered differently from a time continuum of experimenter's clock $T$ on which…
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…
The studied model describes a particle that obeys a one-dimensional nonlinear Schr\"odinger equation in the potential of a double-well. Transitions between the two lowest self-trapped states of this system under the influence of the…
Quantum theory provides a comprehensive framework for quantifying uncertainty, often applied in quantum finance to explore the stochastic nature of asset returns. This perspective likens returns to microscopic particle motion, governed by…
Putting a general, physically relevant upper bound on equilibration times in closed quantum systems is a recently much pursued endeavor. In PRX, 7, 031027 (2017) Garc\'{\i}a-Pintos et al. suggest such a bound. We point out that the general…
An alternative method is proposed for deriving the time dependent Schroedinger equation from the pictures of wave and matrix mechanics. The derivation is of a mixed classical quantum character, since time is treated as a classical variable,…
The symmetry of quantum theory under time reversal has long been a subject of controversy because the transition probabilities given by Born's rule do not apply backward in time. Here, we resolve this problem within a rigorous operational…
This paper considers a main particle and an incident particle classical mechanics elastic collision preserving energy and momentum while ignoring the angular momentum, spin or other particle characteristics. The main result of the paper…
Within the framework of the individuality interpretation of quantum theory (QT), the basic equations of QT cannot be derived from the basic equations of classical mechanics (CM). The unbridgeable gap between CM and QT is given by the fact…
We solve the problem of electron scattering at a potential temporal step discontinuity. We show that the Schrodinger equation cannot account for scattering in this problem, necessitating resort to the Dirac equation, and that breaking gauge…
Several aspects of the time-dependent Schrodinger equation are discussed in the context of Quantum Information Theory.
Exact solutions of time-dependent Schr\"odinger equation in presence of time-dependent potential is defined by point transformation and separation of variables. Energy and Heisenberg uncertainty relation are pursued for time-independent…
A controversy surrounding the "tunnelling time problem" stems from the seeming inability of quantum mechanics to provide, in the usual way, a definition of the duration a particle is supposed to spend in a given region of space. For this…