Related papers: On the Time-Dependent Analysis of Gamow Decay
An analytical solution to the time evolution of decay of one and two identical noninteracting particles is presented using the formalism of resonant states. It is shown that the time-dependent wave function and hence the survival and…
Time evolution of the decay process of unstable particles is investigated in field theory models. We first formulate how to renormalize the non-decay amplitude beyond perturbation theory and then discuss short-time behavior of very…
Deviations of the decay law from exponents are discussing for a long time, however, experimental proofs of such deviations are absent. Here in the general form is shown that the conclusions about non-exponential contributions are due to the…
We present a formalism that represents pure states, mixtures and generalized states as functionals on an algebra containing the observables of the system. Along these states, there are other functionals that decay exponentially at all times…
In this third of a series of four articles, we continue the study of the representations of the hamiltonian dynamical transformations of systems of correlated quantized oscillators. By our use of generalized wave function solutions to…
We consider the initial-value problem for the one-dimensional, time-dependent wave equation with positive, Lipschitz continuous coefficients, which are constant outside a bounded region. Under the assumption of compact support of the…
The description of an open quantum system's decay almost always requires several approximations as to remain tractable. Here, we first revisit the meaning, domain and seeming contradictions of a few of the most widely used of such…
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.…
In the framework of decay theory of Goldberger and Watson we treat $\alpha$-decay of nuclei as a transition caused by a residual interaction between the initial unperturbed bound state and the scattering states with alpha-particle. The…
An analytical solution for the time evolution of decay of two identical non interacting quantum particles seated initially within a potential of finite range is derived using the formalism of resonant states. It is shown that the wave…
A version of the quantum theory of gravity based on the concept of the wave functional of the universe is proposed. To determine the physical wave functional, the quantum principle of least action is formulated as a secular equation for the…
The Wheeler-DeWitt (WdW) equation does not describe any explicit time evolution of the wave function, and somehow related to this issue, there is no natural way of defining an invariant inner product that provides a viable probability…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
The overlap of two wave functions evolving in time with slightly different Hamiltonians decays exponentially, for perturbation strengths greater than the level spacing. We present numerical evidence for a dynamical system that the decay…
We introduce a `proper time' formalism to study the instability of the vacuum in a uniform external electric field due to particle production. This formalism allows us to reduce a quantum field theoretical problem to a quantum-mechanical…
An unstable quantum state generally decays following an exponential law, as environmental decoherence is expected to prevent the decay products from recombining to reconstruct the initial state. Here we show the existence of deviations from…
A quantum mechanical wave of a finite size moves like a classical particle and shows a unique decay probability. Because the wave function evolves according to the Schr\"{o}dinger equation, it preserves the total energy but not the kinetic…
Applying a technique developed in a recent work[1] to calculate wavefunction evolution in a dissipative system with Ohmic friction, we show that the wavelength of the wavefunction decays exponentially, while the Brownian motion width…
In our model of quantum gravity the quantum development of a Cauchy hypersurface is governed by a wave equation derived as the result of a canonical quantization process. To find physically interesting solutions of the wave equation we…
This paper is a pedagogical yet critical introduction to the quantum description of unstable systems, mostly at the level of a graduate quantum mechanics course. Quantum decays appear in many different fields of physics, and their…