Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/9608039

Subtleties in Quantum Mechanical Metastability

R. M. Cavalcanti, C. A. A. de Carvalho

Published Aug 26, 1996• 0 citations
arXivHTMLPDF

Abstract

We present a detailed discussion of some features of quantum mechanical metastability. We analyze the nature of decaying (quasistationary) states and the regime of validity of the exponencial law, as well as decays at finite temperature. We resort to very simple systems and elementary techniques to emphasize subtle aspects of the problem.

DOI
10.48550/arxiv.quant-ph/9608039

Related papers

Metastable states

Kenichi Konishi, Giampiero Paffuti

Abstract In Nature various metastable states appear, i.e., states which, even though they behave like stationary states for a time duration longer than their characteristic periods of quantum motion, after much longer times make transitions to states in the continuum, i.e., decay. It suffices to think of all the excited states of atoms and molecules, or unstable nuclei, to realize the ubiquitous nature of the problem. Many examples of these processes have already been treated in the context of perturbation theory in Section 9.4; an analysis of a particle in external potentials has been made in the semi-classical approximation in Chapter 11.

•Mar 5, 2009•0 citations

On the effectiveness of Gamow's method for calculating decay rates

R. M. Cavalcanti, C. A. A. de Carvalho

We examine Gamow's method for calculating the decay rate of a wave function initially located within a potential well. Using elementary techniques, we examine a very simple, exactly solvable model, in order to show why it is so reliable for calculating decay rates, in spite of its conceptual problems. We also discuss the regime of validity of the exponential decay law.

arXiv:quant-ph/9711037•Nov 19, 1997•9 citations

Time dependence in quantum mechanics—Study of a simple decaying system

D. S. Onley, Anita Kumar

A simple quantum-mechanical model consisting of a two-level system coupled to a continuum, where the interaction can be varied from perturbative to strong, is examined for what can be learned about quantum mechanical decay using elementary methods. The decay spectrum and time dependence of the amplitudes can be calculated in this model, without resorting to perturbation theory. The spectrum is not precisely Lorentzian nor is the decay precisely exponential, features that appear to be shared by all quantum-mechanical models of decaying systems. The conditions for exponential decay and some of the reasons for deviation from this at both short and long times are discussed.

American Journal of Physics•May 1, 1992•71 citations

On the general properties of time-dependent invariants

Qiong-Gui Lin

Several general properties of time-dependent invariants in quantum mechanics are discussed, some of which were not mentioned in the literature.

College Physics•Jan 1, 2005•0 citations

On the interpretation of quantum mechanical weak values

B. E. Y. Svensson

After a brief review of how quantum mechanical weak measurements plus post-selection give rise to the weak value concept, I criticize an interpretation of a weak value as any sort of straightforward, bona fide property of the system under investigation.

Physica Scripta•Dec 1, 2014•10 citations

The dynamics of spontaneous emission

M. Baldo

The spontaneous decay of an excited atom by photon emission is one of the most common and elementary physical process present in nature and in laboratories. The decay is random in time with constant probability density, as it can be inferred by the exponential law observed experimentally. Despite the simplicity of the process, in Quantum Mechanics the decay itself is considered a law of nature which is not further analyzed or explained. However it is legitimate to ask for the reason of its randomness and for the dynamics of the atom around the decay. The decay process of an isolated atom is usually assumed to be instantaneous, the so called Quantum jumps. Particular experimental arrangements can widen the duration of the transition from an excited state to the ground state to a finite time. In general this is due to the quantum back action of the detector. The development of Quantum Optics has enormously enriched the possibilities to study in detail the process, and new illuminating insights have been obtained, but the question is still valid and its answer is still elusive. In this paper we analyze the spontaneous decay within the new prospect introduced by a recent model that complete standard Quantum Mechanics in a formalism which is able to describe the dynamics of measurement and of spontaneous decay. Comparison is made with more phenomenological theories, the Quantum Mechanics of open system and the Stochastic wave function model. In the new model the stochastic photon emission by an excited atom is triggered by the vacuum fluctuations. It is suggested how to re-analyze three types of experiments, already realized in many laboratories, in order to reveal the presence and the effect of these fluctuations.

arXiv:2505.22164•May 28, 2025•0 citations
We present a detailed discussion of some features of quantum mechanical metastability. We analyze the nature of decaying (quasistationary) states and the regime of validity of the exponencial law, as well as decays at finite temperature. We resort to very simple systems and elementary techniques to emphasize subtle aspects of the problem.
Abstract In Nature various metastable states appear, i.e., states which, even though they behave like stationary states for a time duration longer than their characteristic periods of quantum motion, after much longer times make transitions to states in the continuum, i.e., decay. It suffices to think of all the excited states of atoms and molecules, or unstable nuclei, to realize the ubiquitous nature of the problem. Many examples of these processes have already been treated in the context of perturbation theory in Section 9.4; an analysis of a particle in external potentials has been made in the semi-classical approximation in Chapter 11.
A simple quantum-mechanical model consisting of a two-level system coupled to a continuum, where the interaction can be varied from perturbative to strong, is examined for what can be learned about quantum mechanical decay using elementary methods. The decay spectrum and time dependence of the amplitudes can be calculated in this model, without resorting to perturbation theory. The spectrum is not precisely Lorentzian nor is the decay precisely exponential, features that appear to be shared by all quantum-mechanical models of decaying systems. The conditions for exponential decay and some of the reasons for deviation from this at both short and long times are discussed.
The spontaneous decay of an excited atom by photon emission is one of the most common and elementary physical process present in nature and in laboratories. The decay is random in time with constant probability density, as it can be inferred by the exponential law observed experimentally. Despite the simplicity of the process, in Quantum Mechanics the decay itself is considered a law of nature which is not further analyzed or explained. However it is legitimate to ask for the reason of its randomness and for the dynamics of the atom around the decay. The decay process of an isolated atom is usually assumed to be instantaneous, the so called Quantum jumps. Particular experimental arrangements can widen the duration of the transition from an excited state to the ground state to a finite time. In general this is due to the quantum back action of the detector. The development of Quantum Optics has enormously enriched the possibilities to study in detail the process, and new illuminating insights have been obtained, but the question is still valid and its answer is still elusive. In this paper we analyze the spontaneous decay within the new prospect introduced by a recent model that complete standard Quantum Mechanics in a formalism which is able to describe the dynamics of measurement and of spontaneous decay. Comparison is made with more phenomenological theories, the Quantum Mechanics of open system and the Stochastic wave function model. In the new model the stochastic photon emission by an excited atom is triggered by the vacuum fluctuations. It is suggested how to re-analyze three types of experiments, already realized in many laboratories, in order to reveal the presence and the effect of these fluctuations.