College Physics ›› 2026, Vol. 45 ›› Issue (3): 80-.doi: 10.16854/j.cnki.1000-0712.250228

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From probability amplitudes to the quantum age: A century of the Born rule

XING Yongzhong,YUAN Rong,LU Feiping   

  1. Physics Department of Tianshui normal university, Tianshui 741000, Gansu, China
  • Received:2025-04-30 Revised:2025-06-18 Online:2026-05-15 Published:2026-06-04

Abstract: Since Max Born first stated in 1926 that the squared modulus of the wavefunction yields measurement probabilities, the Born rule has withstood a full century of theoretical scrutiny and experimental testing. Guided by the theme “from probability amplitudes to the quantum age,” this paper first reviews the historical setting in which the rule emerged during the transition from the old quantum theory to modern quantum mechanics and shows how it reshaped our understanding of microscopic phenomena. It then gives a concise explanation of the rule’s axiomatic formulation within the Hilbertspace framework. Finally, we outline recent advances in Bornrule research and survey its key applications in presentday quantum technology. 


Key words: Born rule, probability amplitude, measurement probability, centennial