Quantenmechanik der Sto�vorg�nge
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
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?
The wave function was introduced as a guiding field for the motion of particles.
“The concept of the wave function originated in 1924 with de Broglie [ 24 ], who-intrigued by Einstein's idea of the 'Gespensterfeld'-proposed that just as electromagnetic waves are somehow associated with particles, the photons, so should material particles, in particular electrons, be accompanied by waves. He conceived of these waves as 'pilot waves,' somehow governing the motion of the associate”
From Quantum equilibrium and the origin of absolute uncertainty (1992) · cites this paper as [23]
Cited by
Sorted by citations
Zur Theorie des Durchgangs schneller Korpuskularstrahlen durch Materie
Bethe, H. (1930) · Annalen der Physik · doi:10.1002/andp.19303970303 · Cited by 4,076 · see citing works
Über Elementarakte mit zwei Quantensprüngen
Göppert-Mayer, M. (1931) · Annalen der Physik · doi:10.1002/andp.19314010303 · Cited by 2,695 · see citing works
Rovelli, C. (1996) · International Journal of Theoretical Physics · doi:10.1007/bf02302261 · Cited by 1,381 · see citing works
Zur Bremsung rasch bewegter Teilchen beim Durchgang durch Materie
Bloch, F. (1933) · Annalen der Physik · doi:10.1002/andp.19334080303 · Cited by 869 · see citing works
The transactional interpretation of quantum mechanics
Cramer, J. G. (1986) · Reviews of Modern Physics · doi:10.1103/revmodphys.58.647 · Cited by 857 · see citing works
Chemical Applications of X-ray Charge-Density Analysis
Koritsanszky, T. S., & Coppens, P. (2001) · Chemical Reviews · doi:10.1021/cr990112c · Cited by 729 · see citing works
Quantum equilibrium and the origin of absolute uncertainty
D�rr, D., Goldstein, S., & Zangh�, N. (1992) · Journal of Statistical Physics · doi:10.1007/bf01049004 · Cited by 712 · see citing works
Theorie der Beugung von Elektronen an Kristallen
Bethe, H. A. (1928) · Annalen der Physik · doi:10.1002/andp.19283921704 · Cited by 713 · see citing works
Efficient calculation of carrier scattering rates from first principles
Ganose, A. M., Park, J., Faghaninia, A., Woods‐Robinson, R., Persson, K. A., & Jain, A. (2021) · Nature Communications · doi:10.1038/s41467-021-22440-5 · Cited by 700 · see citing works
“[17] A.”
BackgroundMethodClassical and quantum mechanics of the damped harmonic oscillator
Dekker, H. (1981) · Physics Reports · doi:10.1016/0370-1573(81)90033-8 · Cited by 641 · see citing works
Theoretical and experimental aspects of the energy loss of relativistic heavily ionizing particles
Ahlen, S. P. (1980) · Reviews of Modern Physics · doi:10.1103/revmodphys.52.121 · Cited by 581 · see citing works
Electron scattering by ionized impurities in semiconductors
Chattopadhyay, D., & Queisser, H. J. (1981) · Reviews of Modern Physics · doi:10.1103/revmodphys.53.745 · Cited by 585 · see citing works
QUANTUM EQUILIBRIUM AND THE ORIGIN OF ABSOLUTE UNCERTAINTY
D�rr, D., Goldstein, S., & Zangh�, N. (2015) · Cited by 555 · see citing works
Quantum Mechanics and Radioactive Disintegration
Gurney, R. W., & Condon, E. U. (1929) · Physical Review · doi:10.1103/physrev.33.127 · Cited by 420 · see citing works
Coecke, B., & Kissinger, A. (2017) · Cambridge University Press eBooks · doi:10.1017/9781316219317 · Cited by 427 · see citing works
On the Scattering of a Particle by a Static Potential
Jost, R., & Pais, A. (1951) · Physical Review · doi:10.1103/physrev.82.840 · Cited by 370 · see citing works
Concepts of quantum non-Markovianity: A hierarchy
Li, L., Hall, M. J. W., & Wiseman, H. M. (2018) · Physics Reports · doi:10.1016/j.physrep.2018.07.001 · Cited by 390 · see citing works
“the text book [5]), a term which has its origins in scattering theory [38].”
BackgroundFrench, S., & Krause, D. (2006) · doi:10.1093/0199278245.001.0001 · Cited by 339 · see citing works
Differentiable learning of quantum circuit Born machines
Liu, J.-G., & Wang, L. (2018) · Physical Review A · doi:10.1103/physreva.98.062324 · Cited by 279 · see citing works
The Low-Energy Scattering of Electrons and Positrons by Hydrogen Atoms
Burke, P. G., & Smith, K. (1962) · Reviews of Modern Physics · doi:10.1103/revmodphys.34.458 · Cited by 274 · see citing works
The Quantitative Study of the Collisions of Electrons with Atoms
Brode, R. B. (1933) · Reviews of Modern Physics · doi:10.1103/revmodphys.5.257 · Cited by 259 · see citing works
Conceptual Developments of 20th Century Field Theories
Cao, T. Y. (1997) · Cambridge University Press eBooks · doi:10.1017/cbo9780511563997 · Cited by 245 · see citing works
Is a System’s Wave Function in One-to-One Correspondence with Its Elements of Reality?
Colbeck, R., & Renner, R. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.150402 · Cited by 245 · see citing works
The scattering of fast electrons by crystals
Humphreys, C. J. (1979) · Reports on Progress in Physics · doi:10.1088/0034-4885/42/11/002 · Cited by 239 · see citing works
Electrical Discharges in Gases. Part I. Survey of Fundamental Processes
Compton, K. T., & Langmuir, I. (1930) · Reviews of Modern Physics · doi:10.1103/revmodphys.2.123 · Cited by 211 · see citing works
Quantum Theory without Observers—Part One
Goldstein, S. (1998) · Physics Today · doi:10.1063/1.882184 · Cited by 201 · see citing works
Budroni, C., Cabello, A., Gühne, O., Kleinmann, M., & Larsson, J.-Å. (2022) · Reviews of Modern Physics · doi:10.1103/revmodphys.94.045007 · Cited by 232 · see citing works
Introduction to Some Recent Work in Meson Theory
Wick, G. C. (1955) · Reviews of Modern Physics · doi:10.1103/revmodphys.27.339 · Cited by 192 · see citing works
The Potential of Using Quantum Theory to Build Models of Cognition
Wang, Z., Busemeyer, J. R., Harald Atmanspacher, A., & Pothos, E. M. (2013) · Topics in Cognitive Science · doi:10.1111/tops.12043 · Cited by 186 · see citing works
“Born's rule (Born, 1926), which defines the probability to measure a certain quantum state by the squared magnitude of its amplitude, therefore entails interference terms that are absent in classical probability theory.”
BackgroundThe timelessness of quantum gravity: II. The appearance of dynamics in static configurations
Barbour, J. (1994) · Classical and Quantum Gravity · doi:10.1088/0264-9381/11/12/006 · Cited by 179 · see citing works
On the Quantum Theory of Electronic Impacts
Oppenheimer, J. R. (1928) · Physical Review · doi:10.1103/physrev.32.361 · Cited by 180 · see citing works
Dragsdorf, R. D. (1956) · Journal of Applied Physics · doi:10.1063/1.1722443 · Cited by 172 · see citing works
Bates, D. R., Fundaminsky, A., Leech, J. W., et al. (1950) · Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences · doi:10.1098/rsta.1950.0015 · Cited by 170 · see citing works
Global mantle structure from multifrequency tomography using P, PP and P-diffracted waves
Hosseini, K., Sigloch, K., Tsekhmistrenko, M., et al. (2019) · Geophysical Journal International · doi:10.1093/gji/ggz394 · Cited by 167 · see citing works
“Dahlen et al. (2000) developed a method to efficiently calculate sensitivity kernels KT using paraxial approximation in conjunction with ray theory and the Born approximation (Born 1926).”
MethodMadison, D. H., & Shelton, W. N. (1973) · Physical Review A · doi:10.1103/physreva.7.499 · Cited by 165 · see citing works
Do We Really Understand Quantum Mechanics?
Laloë, F. (2012) · Cambridge University Press eBooks · doi:10.1017/9781108569361 · Cited by 158 · see citing works
Hertel, I. V., Schmidt, H., Bähring, A., et al. (1985) · Reports on Progress in Physics · doi:10.1088/0034-4885/48/3/003 · Cited by 155 · see citing works
The Stability of Matter: From Atoms to Stars
Lieb, E. H. (1991) · Springer eBooks · doi:10.1007/978-3-662-02725-7 · Cited by 150 · see citing works
Brookes, D. T., & Etkina, E. (2007) · Physical Review Special Topics - Physics Education Research · doi:10.1103/physrevstper.3.010105 · Cited by 149 · see citing works
Scaled plane-wave Born cross sections for atoms and molecules
Tanaka, H., Brunger, M. J., Campbell, L., et al. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.025004 · Cited by 149 · see citing works
The equivalence myth of quantum mechanics —Part I
Müller, F. (1997) · Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics · doi:10.1016/s1355-2198(96)00022-6 · Cited by 140 · see citing works
“I5 First conceived by Born (1926) The Unresolved Quantum Dilemma 3.”
A Review of Computational Methods in Materials Science: Examples from Shock-Wave and Polymer Physics
Steinhauser, M. O., & Hiermaier, S. J. (2009) · International Journal of Molecular Sciences · doi:10.3390/ijms10125135 · Cited by 138 · see citing works
The stability of matter: from atoms to stars
Lieb, É. H. (1990) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-1990-15831-8 · Cited by 135 · see citing works
Bush, J. W. M., & Oza, A. U. (2020) · Reports on Progress in Physics · doi:10.1088/1361-6633/abc22c · Cited by 133 · see citing works
Howard, D. A. (1990) · NATO ASI series. Series B : Physics · doi:10.1007/978-1-4684-8771-8_6 · Cited by 129 · see citing works
“Remember that it was Born himself who earlier in the summer of 1926 had first introduced the probabilistic interepretation of the Schrodinger wave function (Born 1926a, 1926b).”
BackgroundBeisbart, C., & Hartmann, S. (2011) · doi:10.1093/acprof:oso/9780199577439.001.0001 · Cited by 134 · see citing works
Time scales for dynamical relaxation to the Born rule
Towler, M. D., Russell, N. J., & Valentini, A. (2011) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2011.0598 · Cited by 117 · see citing works
Electron-Electron Scattering and Transport Phenomena in Nonpolar Semiconductors
Appel, J. (1961) · Physical Review · doi:10.1103/physrev.122.1760 · Cited by 114 · see citing works
A trajectory-based understanding of quantum interference
Sanz, Á. S., & Miret-Artés, S. (2008) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/41/43/435303 · Cited by 104 · see citing works
Quantum Mechanics of Collision Processes I. scattering of particles in a definite force field
Condon, E. U., & Morse, P. Μ. (1931) · Reviews of Modern Physics · doi:10.1103/revmodphys.3.43 · Cited by 103 · see citing works
Atom–surface diffraction: a trajectory description
Guantes, R., Sanz, Á. S., Margalef-Roig, J., & Miret-Artés, S. (2004) · Surface Science Reports · doi:10.1016/j.surfrep.2004.02.001 · Cited by 100 · see citing works
Statistical Interpretation of Quantum Mechanics
Born, M. (1955) · Science · doi:10.1126/science.122.3172.675 · Cited by 101 · see citing works
Self-citationThe equivalence myth of quantum mechanics—part II
Müller, F. (1997) · Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics · doi:10.1016/s1355-2198(97)00001-4 · Cited by 96 · see citing works
Ensemble interpretations of quantum mechanics. A modern perspective
Home, D., & Whitaker, M. A. B. (1992) · Physics Reports · doi:10.1016/0370-1573(92)90088-h · Cited by 97 · see citing works
The Scattering of Slow Electrons by Neutral Atoms
Feenberg, E. (1932) · Physical Review · doi:10.1103/physrev.40.40 · Cited by 95 · see citing works
Shera, C. A., Tubis, A., & Talmadge, C. L. (2005) · The Journal of the Acoustical Society of America · doi:10.1121/1.1895025 · Cited by 94 · see citing works
Der Energieimpulssatz der Materiewellen
Schrödinger, E. (1927) · Annalen der Physik · doi:10.1002/andp.19273870211 · Cited by 93 · see citing works
Calculation and tabulation of mott cross‐sections for large‐angle electron scattering
Reimer, L., & Lödding, B. (1984) · Scanning · doi:10.1002/sca.4950060303 · Cited by 93 · see citing works
Electron–positron pair production by photons: A historical overview
Hubbell, J. H. (2005) · Radiation Physics and Chemistry · doi:10.1016/j.radphyschem.2005.10.008 · Cited by 92 · see citing works
The Theory of the Universal Wave Function
Barrett, J. A. (2001) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780199247431.003.0003 · Cited by 105 · see citing works
Looking at Molecular Orbitals in Three-Dimensional Form: From Dream to Reality
Takahashi, M. (2009) · Bulletin of the Chemical Society of Japan · doi:10.1246/bcsj.82.751 · Cited by 89 · see citing works
Plural Scattering of 20-kev Electrons in Aluminum
Marton, L., Simpson, J. A., Fowler, H. A., et al. (1962) · Physical Review · doi:10.1103/physrev.126.182 · Cited by 89 · see citing works
Biology and medicine in the landscape of quantum advantages
Cordier, B. A., Sawaya, N. P. D., Guerreschi, G. G., & McWeeney, S. K. (2022) · Journal of The Royal Society Interface · doi:10.1098/rsif.2022.0541 · Cited by 87 · see citing works
“The Born rule [38] states that the probability of measuring each basis state corresponds to the magnitude-squared of their probability amplitude,”
BackgroundExperimental evidence of quantum randomness incomputability
Calude, C. S., Dinneen, M. J., Dumitrescu, M. E. B., & Svozil, K. (2010) · Physical Review A · doi:10.1103/physreva.82.022102 · Cited by 84 · see citing works
“[2] Max Born, “Quantenmechanik der Stoßvorgänge,” Zeitschrift für Physik, 38, 803–827 (1926).”
BackgroundEnergieaustausch nach der Wellenmechanik
Schrödinger, E. (1927) · Annalen der Physik · doi:10.1002/andp.19273881504 · Cited by 77 · see citing works
On the Convergence of Born Expansions
Kohn, W. (1954) · Reviews of Modern Physics · doi:10.1103/revmodphys.26.292 · Cited by 75 · see citing works
Quantum Theory without Observers—Part Two
Goldstein, S. (1998) · Physics Today · doi:10.1063/1.882241 · Cited by 72 · see citing works
Born's probabilistic interpretation: A case study of ‘concepts in flux’
Beller, M. (1990) · Studies in History and Philosophy of Science Part A · doi:10.1016/0039-3681(90)90033-5 · Cited by 70 · see citing works
Travel-time sensitivity kernels in ocean acoustic tomography
Skarsoulis, E. K., & Cornuelle, B. D. (2004) · The Journal of the Acoustical Society of America · doi:10.1121/1.1753292 · Cited by 70 · see citing works
The Investigation of Electron Distribution in Atoms by Electron Diffraction
Bartell, L. S., & Brockway, L. O. (1953) · Physical Review · doi:10.1103/physrev.90.833 · Cited by 68 · see citing works
Spontaneous and stimulated emissions of a preformed quantum free-electron wave function
Pan, Y., & Gover, A. (2019) · Physical Review A · doi:10.1103/physreva.99.052107 · Cited by 67 · see citing works
Accurate one-dimensional inverse scattering using a nonlinear renormalization technique
Jaggard, D. L., & Kim, Y. (1985) · Journal of the Optical Society of America A · doi:10.1364/josaa.2.001922 · Cited by 67 · see citing works
A concise history of mainstream seismology: Origins, legacy, and perspectives
Ben‐Menahem, A. (1995) · Bulletin of the Seismological Society of America · doi:10.1785/bssa0850041202 · Cited by 66 · see citing works
Zur Quantenmechanik der Richtungsentartung
Oppenheimer, J. R. (1927) · The European Physical Journal A · doi:10.1007/bf01397228 · Cited by 66 · see citing works
Truhlar, D. G., Rice, J. K., Kuppermann, A., et al. (1970) · Physical Review A · doi:10.1103/physreva.1.778 · Cited by 66 · see citing works
Probability out of Determinism
Strevens, M. (2011) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780199577439.003.0013 · Cited by 65 · see citing works
Weimar Culture and Quantum Causality
Hendry, J. (1980) · History of Science · doi:10.1177/007327538001800301 · Cited by 63 · see citing works
Picard, G., Löwe, H., Dominé, F., et al. (2022) · AGU Advances · doi:10.1029/2021av000630 · Cited by 62 · see citing works
Mustroph, H. (2016) · ChemPhysChem · doi:10.1002/cphc.201600243 · Cited by 61 · see citing works
The born expansion in non-relativistic quantum theory
Zemach, C., & Klein, A. (1958) · Il Nuovo Cimento · doi:10.1007/bf02859570 · Cited by 61 · see citing works
Single-particle Schrödinger fluid. I. Formulation
Kan, K.-K., & Griffin, J. J. (1977) · Physical Review C · doi:10.1103/physrevc.15.1126 · Cited by 60 · see citing works
Ionen- und Atomquerschnitte im Plasma verschiedener Gase
Maecker, H., Peters, T., & Schenk, H. (1955) · The European Physical Journal A · doi:10.1007/bf01349371 · Cited by 60 · see citing works
On the Tacit Linearity Assumption in Common Cascaded Models of RIS-Parametrized Wireless Channels
Rabault, A., Magoarou, L. L., Sol, J., et al. (2024) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2024.3367953 · Cited by 59 · see citing works
“(8), we obtain a Born series : A Born series is the expansion of a scattering quantity in terms of the interaction potential, named after Max Born who studied particles in scattering potentials in quantum mechanics [5], [22].”
MethodJacobsen, C. J. (2019) · Cambridge University Press eBooks · doi:10.1017/9781139924542 · Cited by 62 · see citing works
Aperture scanning Fourier ptychographic microscopy
Ou, X., Chung, J., Horstmeyer, R. W., et al. (2016) · Biomedical Optics Express · doi:10.1364/boe.7.003140 · Cited by 56 · see citing works
On the direct observability of quantum waves
Selleri, F. (1982) · Foundations of Physics · doi:10.1007/bf01300548 · Cited by 56 · see citing works
A simplified genesis of quantum mechanics
Darrigol, O. (2009) · Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics · doi:10.1016/j.shpsb.2009.03.001 · Cited by 55 · see citing works
Ab initioelectronic stopping power of protons in bulk materials
Shukri, A. A., Bruneval, F., & Reining, L. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.93.035128 · Cited by 54 · see citing works
Reinisch, G. (1994) · Physica A Statistical Mechanics and its Applications · doi:10.1016/0378-4371(94)90128-7 · Cited by 51 · see citing works
Duncan, A., & Janssen, M. (2009) · Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics · doi:10.1016/j.shpsb.2009.07.001 · Cited by 50 · see citing works
Inverse electromagnetic scattering models for sea ice
Golden, K. M., Borup, D. T., Cheney, M., et al. (1998) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/36.718638 · Cited by 50 · see citing works
The puzzle of canonical transformations in early quantum mechanics
Lacki, J. (2004) · Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics · doi:10.1016/j.shpsb.2003.07.001 · Cited by 49 · see citing works
Aerts, D., & de Bianchi, M. S. (2014) · Annals of Physics · doi:10.1016/j.aop.2014.09.020 · Cited by 49 · see citing works
“According to the former, the solution of the problem is equivalent to its elimination: quantum probabilities are not required to be further explained, as what really matters in a physical theory is its predictive power, expressed by means of a rule of correspondence between the formalism of the theory and the results…”
BackgroundThree criteria for quantum random-number generators based on beam splitters
Svozil, K. (2009) · Physical Review A · doi:10.1103/physreva.79.054306 · Cited by 48 · see citing works
Einstein's 1927 unpublished hidden-variable theory: Its background, context and significance
Belousek, D. W. S. (1996) · Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics · doi:10.1016/s1355-2198(96)00015-9 · Cited by 47 · see citing works
Models and methodologies in current theoretical high-energy physics
Cushing, J. T. (1982) · Synthese · doi:10.1007/bf00413723 · Cited by 46 · see citing works
(Never) Mind your p’s and q’s: Von Neumann versus Jordan on the foundations of quantum theory
Duncan, A., & Michel Janssen, B. (2012) · The European Physical Journal H · doi:10.1140/epjh/e2012-30024-5 · Cited by 45 · see citing works
Bell, K. L., & Kingston, A. E. (1974) · Advances in atomic and molecular physics · doi:10.1016/s0065-2199(08)60347-4 · Cited by 46 · see citing works
Manageable multidimensional inverse scattering theory
Bates, R. H. T., Smith, V. A., & Murch, R. (1991) · Physics Reports · doi:10.1016/0370-1573(91)90026-i · Cited by 45 · see citing works
Heisenberg and the wave–particle duality
Camilleri, K. (2006) · Studies in History and Philosophy of Science Part B Studies in History and Philosophy of Modern Physics · doi:10.1016/j.shpsb.2005.08.002 · Cited by 44 · see citing works
- Authors
- Born, M.
- Corresponding author
- Born, Max
- Venue
- Zeitschrift f�r Physik
- Published
- 1926-11
- Volume
- 38
- Issue
- 11-12
- Pages
- 803-827
- ISSN
- 1434-6001 (ISSN-L)
- 1434-601X
- OpenAlex
- W1989868128
- Cited by
- 956
- References
- 0
- Citations by year
- 2026: 44 · 2025: 78 · 2024: 56 · 2023: 36 · 2022: 37 · 2021: 40 · 2020: 31 · 2019: 94 · 2018: 33 · 2017: 26 · 2016: 19 · 2015: 12 · 2014: 13 · 2013: 11 · 2012: 34
- FWCI
- 13.02
- Type
- journal article
- Language
- de
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- The European Physical Journal A (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
- Keywords
- scattering theory, transition probabilities, eigenfunctions, Schrödinger equation
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