The DOI matches its Crossref record; 53 of the 53 references it cites were found in a registry or an index.
Decay theory of unstable quantum systems
Open accessAbstract
The present review article is aimed at a clear formulation of the basic problematics of the decay and at a description of the various recent attempts to solve this delicate problem, illustrating both their successes and limitations. The organisation of the article is as follows. After a short summary of the classical description of the decay, a detailed study of the quantum non-decay probability is given. Then the peculiar dynamical situation leading to the formation of an unstable system is identified and the formal and physical aspects of the process are discussed. A detailed analysis is then made of the preparation procedure of an unstable system which is shown to amount to a localisation of the decay fragments within a distance of the order of the range of the forces acting between them. After this the discussion of the general properties of the non-decay probability at all times is completed.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“Most of the previous results in this field [1, 2, 3] trace back to the time-energy uncertainty relation in the form derived by Mandelstam and Tamm [4]: in this way, the various lifetimes are bounded by the energy spread ∆ E of the system.”
From Quantum limits to dynamical evolution (2003) · cites this paper as [4]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Zur Quantentheorie des Atomkernes
Gamow, G. (1928) · The European Physical Journal A · doi:10.1007/bf01343196 · Cited by 2,336
Berechnung der nat�rlichen Linienbreite auf Grund der Diracschen Lichttheorie
Weisskopf, V. F., & Wigner, E. P. (1930) · The European Physical Journal A · doi:10.1007/bf01336768 · Cited by 1,817
�ber die nat�rliche Linienbreite in der Strahlung des harmonischen Oszillators
Weisskopf, V. F., & Wigner, E. P. (1930) · The European Physical Journal A · doi:10.1007/bf01397406 · Cited by 435
Quantum Mechanics and Radioactive Disintegration
Gurney, R. W., & Condon, E. U. (1929) · Physical Review · doi:10.1103/physrev.33.127 · Cited by 432
Coupled Anharmonic Oscillators. I. Equal-Mass Case
Banks, T., Bender, C. M., & Wu, T. T. (1973) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.8.3346 · Cited by 249
Davies, E. B. (1969) · Communications in Mathematical Physics · doi:10.1007/bf01645529 · Cited by 243
A unitarity bound on the evolution of nonstationary states
Fleming, G. N. (1973) · Il Nuovo Cimento A · doi:10.1007/bf02819419 · Cited by 218
Evolution of a Quasi-Stationary State
Winter, R. G. (1961) · Physical Review · doi:10.1103/physrev.123.1503 · Cited by 187
Relaxation Phenomena in Spin and Harmonic Oscillator Systems
Rau, J. (1963) · Physical Review · doi:10.1103/physrev.129.1880 · Cited by 152
Field theory of unstable particles
Schwinger, J. (1960) · Annals of Physics · doi:10.1016/0003-4916(60)90027-0 · Cited by 124
Does the lifetime of an unstable system depend on the measuring apparatus?
Degasperis, A., Fonda, L., & Ghirardi, G. C. (1974) · Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields · doi:10.1007/bf02731351 · Cited by 122
Self-citationLifetime and Decay of Unstable Particles in S -Matrix Theory
Goldberger, M. L., & Watson, K. (1964) · Physical Review · doi:10.1103/physrev.136.b1472 · Cited by 114
Mass and Lifetime of Unstable Particles
Jacob, R., & Sachs, R. G. (1961) · Physical Review · doi:10.1103/physrev.121.350 · Cited by 111
On the quantum foundations of the exponential decay law
Fonda, L., Ghirardi, G. C., Rimini, A., & Weber, T. (1973) · Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields · doi:10.1007/bf02748082 · Cited by 108
Self-citationA model of an unstable particle
Glaser, V., & Källén, G. (1956) · Nuclear Physics · doi:10.1016/0029-5582(56)90116-x · Cited by 100
�ber die Exponentialn�herung beim Teilchenzerfall
H�hler, G. (1958) · The European Physical Journal A · doi:10.1007/bf01375212 · Cited by 100
On a reinterpretation of decay experiments
Ekstein, H., & Siegert, A. J. F. (1971) · Annals of Physics · doi:10.1016/0003-4916(71)90133-3 · Cited by 87
Williams, D. N. (1971) · Communications in Mathematical Physics · doi:10.1007/bf01645753 · Cited by 84
Relativistic Theory of Unstable Particles. II
Matthews, P. T., & Salam, A. (1959) · Physical Review · doi:10.1103/physrev.115.1079 · Cited by 71
Horwitz, L. P., LaVita, J. A., & Marchand, J.-P. (1971) · Journal of Mathematical Physics · doi:10.1063/1.1665570 · Cited by 71
The exponential decay law of unstable systems
Newton, R. G. (1961) · Annals of Physics · doi:10.1016/0003-4916(61)90060-4 · Cited by 61
Double Poles and Nonexponential Decays
Bell, J. S., & Goebel, C. J. (1965) · Physical Review · doi:10.1103/physrev.138.b1198 · Cited by 61
On the validity of the exponential law for the decay of an unstable particle
Lévy, M. M. (1959) · Il Nuovo Cimento · doi:10.1007/bf02726390 · Cited by 60
The Decay of Resonance Radiation by Spontaneous Emission
Hellund, E. J. (1953) · Physical Review · doi:10.1103/physrev.89.919 · Cited by 45
Some remarks on the origin of the deviations from the exponential decay law of an unstable particle
Fonda, L., & Ghirardi, G. C. (1972) · Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields · doi:10.1007/bf02728686 · Cited by 42
Self-citationWie gut gilt das Exponentialgesetz beim ?-Zerfall?
Petzold, J. (1959) · The European Physical Journal A · doi:10.1007/bf01333122 · Cited by 41
Wave Packet Theory of Scattering
Ohmura, T. (1964) · Progress of Theoretical Physics Supplement · doi:10.1143/ptps.29.108 · Cited by 39
Correspondence between Unstable Particles and Poles in S -Matrix Theory
Calucci, G., Fonda, L., & Ghirardi, G. C. (1968) · Physical Review · doi:10.1103/physrev.166.1719 · Cited by 39
Self-citationOn the Radiation Damping and the Decay of an Excited State
Namiki, M., & Mugibayashi, N. (1953) · Progress of Theoretical Physics · doi:10.1143/ptp.10.474b · Cited by 33
On the physical interpretation of complex poles of theS-matrix — II
Nussenzveig, H. M. (1961) · Il Nuovo Cimento · doi:10.1007/bf02731560 · Cited by 32
Peres, A. (1966) · Annals of Physics · doi:10.1016/0003-4916(66)90038-8 · Cited by 32
Unstable particles and the poincaré semigroup
Schulman, L. S. (1970) · Annals of Physics · doi:10.1016/0003-4916(70)90400-8 · Cited by 32
On the exponential decay law of nonstable particle
Terent'ev, M. V. (1972) · Annals of Physics · doi:10.1016/0003-4916(72)90259-x · Cited by 31
On the quantum foundations of the exponential decay law
Fonda, L., Ghirardi, G. C., Rimini, A., & Weber, T. (1973) · Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields · doi:10.1007/bf02727595 · Cited by 29
Self-citationCorrespondence between Unstable Particles and Poles in S -Matrix Theory: The Exponential Decay Law
Calucci, G., & Ghirardi, G. C. (1968) · Physical Review · doi:10.1103/physrev.169.1339 · Cited by 21
Self-citationParticle localization in field theory
Steinmann, O. (1968) · Communications in Mathematical Physics · doi:10.1007/bf01648330 · Cited by 20
Evolution of quantum systems subject to random measurements
Fonda, L., Ghirardi, G. C., & Rimini, A. (1973) · Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B · doi:10.1007/bf02832636 · Cited by 17
Self-citationContribution to the decay theory of unstable quantum systems
Fonda, L., & Ghirardi, G. C. (1970) · Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields · doi:10.1007/bf02725177 · Cited by 17
Self-citationA Critical Discussion on the Decay of Quantum Unstable Systems
Fonda, L. (1977) · Fortschritte der Physik · doi:10.1002/prop.19770250104 · Cited by 15
Self-citationZum Anfangswertproblem zerfallender Zust�nde
Petzold, J. (1959) · The European Physical Journal A · doi:10.1007/bf01375156 · Cited by 14
Interpretation of the Normalizable State in the Lee Model with Form Factor
Fonda, L., Ghirardi, G. C., & Rimini, A. (1964) · Physical Review · doi:10.1103/physrev.133.b196 · Cited by 13
Self-citationAlzetta, R., & D'Ambrogio, E. (1966) · Nuclear Physics · doi:10.1016/0029-5582(66)90484-6 · Cited by 11
Fonda, L., & Ghirardi, G. C. (1972) · Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields · doi:10.1007/bf02899781 · Cited by 11
Self-citationContribution to the decay theory of unstable quantum systems. — II
Fonda, L., & Ghirardi, G. C. (1971) · Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields · doi:10.1007/bf02723386 · Cited by 10
Self-citationOn the Connection between Particles and Poles of the S‐Matrix
Fonda, L. (1972) · Fortschritte der Physik · doi:10.1002/prop.19720200204 · Cited by 10
Self-citationA Method of Renormalization for Unstable Particles
Okabayashi, T., & Sato, S. (1957) · Progress of Theoretical Physics · doi:10.1143/ptp.17.30 · Cited by 10
Number of wave functions of unstable particle
Jersák, J. (1969) · Cited by 9
Unstable systems and measurement processes
Ali, S., & Ghirardi, G. C. (1974) · Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields · doi:10.1007/bf02748205 · Cited by 8
Self-citationNo-Pole S -Matrix Fit to the Δ(1236) Resonance
Fonda, L., Ghirardi, G. C., & Shaw, G. L. (1973) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.8.353 · Cited by 8
Self-citationOn the quantum mechanical treatment of decaying non-relativistic systems
Lanz, L., Lugiato, L. A., & Ramella, G. (1973) · International Journal of Theoretical Physics · doi:10.1007/bf00687091 · Cited by 7
Fonda, L., Ghirardi, G. C., & Rimini, A. (1975) · Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields · doi:10.1007/bf02729298 · Cited by 6
Self-citationDetection of the Poles of an Amplitude: A Comment on a Recent Paper
Calucci, G., & Ghirardi, G. C. (1972) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.6.3346 · Cited by 3
Self-citationK2 → 2π decay and possible CP-nonconservation
Terent'ev, M. V. (1965) · Uspekhi Fizicheskih Nauk · doi:10.3367/ufnr.0086.196506b.0231 · Cited by 3
Research works printed but not linked: 11
- Ali S T, 1975, Nuovo Cim., 25A, 134
- Beskow A, 1967, Ark. Fys., 34, 561
- Brzeski A, 1975, Acta. Phys. Polon., 6, 577
- Davies E B, 1975, Helv. Phys. Acta., 48, 365
- Ersak I, 1969, Yad. Fiz., 9, 458
- Ersak I, Sov. J. Nucl. Phys., 9, 263
- Garczynski, 1976, Acta. Phys. Polon., 7, 627
- Khalfin L A, 1957, Zh. Eksp. Teor. Fiz., 33, 1371
- Khalfin L A, 1958, Sov. Phys.-JETP, 6, 1053
- Krylov N S, 1947, Zh. Eksp. Teor. Fiz., 17, 93
- Sinha K, 1972, Helv. Phys. Acta., 45, 619
Cited by
Sorted by citations
Reaction-rate theory: fifty years after Kramers
Hänggi, P., Talkner, P., & Borkovec, M. (1990) · Reviews of Modern Physics · doi:10.1103/revmodphys.62.251 · Cited by 6,154
Environment-induced superselection rules
Zurek, W. H. (1982) · Physical Review D · doi:10.1103/physrevd.26.1862 · Cited by 1,415
Quantum-optical analogies using photonic structures
Longhi, S. (2009) · Laser & Photonics Reviews · doi:10.1002/lpor.200810055 · Cited by 718
Bassi, A., & Ghirardi, G. (2003) · Physics Reports · doi:10.1016/s0370-1573(03)00103-0 · Cited by 725
Self-citationQuantum Electrodynamics of Strong Fields
Reinhardt, J., Greiner, W., Reinhardt, J., & Greiner, W. (1983) · Springer eBooks · doi:10.1007/978-1-4899-2139-0 · Cited by 683
Metadata
- Authors
- Fonda, L., Ghirardi, G. C., & Rimini, A.
- Affiliations
- University of Trieste (IT)
- Venue
- Reports on Progress in Physics
- Publisher
- IOP Publishing
- Published
- 1978-04-01
- Volume
- 41
- Issue
- 4
- Pages
- 587-631
- ISSN
- 0034-4885 (ISSN-L)
- 1361-6633
- OpenAlex
- W1973778620
- Cited by
- 627
- References
- 53
- Citations by year
- 2026: 13 · 2025: 12 · 2024: 15 · 2023: 11 · 2022: 13 · 2021: 15 · 2020: 54 · 2019: 19 · 2018: 24 · 2017: 18 · 2016: 19 · 2015: 19 · 2014: 19 · 2013: 19 · 2012: 16
- FWCI
- 6.61
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Reports on Progress in Physics (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Nuclear physics research studies
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
- Keywords
- quantum decay, unstable quantum systems
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
