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Hilbrand J. Groenewold

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573: 639: 586: 579: 201:. In 1951, he obtained a position in Groningen in theoretical physics, first as a lecturer, then as a senior lecturer, and finally as a professor in 1955. He was the initiator and organizer of the Vosbergen Conference in the Netherlands for over two decades. 279:
A very early piece that anticipated several key ideas of existential risk. It failed to reach a wide audience, leaving these ideas in obscurity until they were independently discovered decades later.
220:, the cornerstone of this formulation of the theory, ironically often also associated with Moyal's name, even though it is not featured in Moyal's papers and was not fully understood by Moyal. 515: 267: 216:
as an invertible transform, rather than as an unsatisfactory quantization rule. Significantly, this work further formulated and first appreciated the all-important
725: 623: 246:. This observation and his counterexamples contrasting Poisson brackets to commutators have been generalized and codified to what is now known as the 193:, and several addresses in the North of the Netherlands during World War II, he earned his Ph.D. degree in 1946, under the tutelage of 676: 616: 720: 705: 550: 609: 463:
Induction, Physics, and Ethics: Proceedings and Discussions of the 1968 Salzburg Colloquium in the Philosophy of Science
181:, with a major in physics and minors in mathematics and mechanics in 1934. After a visit to Cambridge to interact with 85: 730: 255: 524: 423: 715: 710: 735: 486: 669: 556: 213: 740: 272: 185:(1934–5) on the links between classical and quantum mechanics, and a checkered career working with 662: 205: 178: 158: 93: 650: 597: 470: 457: 275:
in Groenewold's 1968 paper "Modern Science and Social Responsibility", which Ord described as:
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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
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H.J. Groenewold (1946), "On the principles of elementary quantum mechanics",
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Curtright, T. L.; Zachos, C. K. (2012). "Quantum Mechanics in Phase Space".
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Moreover, Groenewold first understood and demonstrated that the
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The Precipice: Existential Risk and the Future of Humanity
410:. Graduate Texts in Mathematics. Vol. 267. Springer. 268:
The Precipice: Existential Risk and the Future of Humanity
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who pioneered the largely operator-free formulation of
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For one version of this result, see Theorem 13.13 in:
456: 687: 366:"The Fundamental Equations of Quantum Mechanics" 271:, identified a pioneering discussion of general 204:His 1946 thesis paper laid the foundations of 461:. In Weingartner, Paul; Zecha, Gerhard (eds.). 318: 726:Academic staff of the University of Groningen 670: 617: 553:from U Groningen memorial conference, 2016. 677: 663: 624: 610: 592:This article about a Dutch scientist is a 458:"Modern science and social responsibility" 454: 389: 332: 236:cannot be made to faithfully correspond 169:Groenewold was born on 29 June 1910 in 16:Dutch theoretical physicist (1910–1996) 688: 189:in Groningen, then Leiden, the Hague, 363: 645:This article about a physicist is a 633: 566: 405: 509: 13: 14: 752: 544: 519:. London: Bloomsbury Publishing. 455:Groenewold, Hilbrand J. (1970) . 408:Quantum Theory for Mathematicians 637: 584: 577: 571: 206:quantum mechanics in phase space 465:. Synthese library. Dordrecht: 321:Asia Pacific Physics Newsletter 721:University of Groningen alumni 503: 448: 398: 357: 312: 289: 1: 706:20th-century Dutch physicists 308:10.1016/S0031-8914(46)80059-4 283: 208:, in unwitting parallel with 649:. You can help Knowledge by 596:. You can help Knowledge by 479:10.1007/978-94-010-3305-3_19 242:, as had been envisioned by 164: 33:Hilbrand Johannes Groenewold 7: 234:, and thus that the latter 10: 757: 632: 565: 731:Utrecht University alumni 416:10.1007/978-1-4614-7116-5 343:10.1142/S2251158X12000069 128: 116: 106: 99: 81: 57: 28: 21: 364:Dirac, P. A. M. (1925). 273:global catastrophic risk 177:. He graduated from the 159:phase-space quantization 145:(1910–1996) was a Dutch 716:People from Menterwolde 711:Mathematical physicists 406:Hall, Brian C. (2013). 179:University of Groningen 94:Phase-space formulation 90:Weyl–Groenewold product 391:10.1098/rspa.1925.0150 281: 23:Hilbrand J. Groenewold 736:Dutch scientist stubs 557:Alternate open source 277: 227:is isomorphic to the 214:Wigner–Weyl transform 147:theoretical physicist 559:of the 1946 article. 256:Groenewold's theorem 86:Groenewold's theorem 382:1925RSPSA.109..642D 265:, in his 2020 book 173:in the province of 199:Utrecht University 658: 657: 605: 604: 551:Biographical note 258:for one version. 151:quantum mechanics 135:Hilbrand Johannes 132: 131: 101:Scientific career 748: 679: 672: 665: 641: 634: 626: 619: 612: 588: 583: 582: 581: 575: 567: 539: 538: 507: 501: 500: 460: 452: 446: 445: 402: 396: 395: 393: 376:(752): 642–653. 361: 355: 354: 336: 316: 310: 293: 183:John von Neumann 118:Doctoral advisor 67: 65: 62:23 November 1996 42: 40: 19: 18: 756: 755: 751: 750: 749: 747: 746: 745: 741:Physicist stubs 686: 685: 684: 683: 631: 630: 576: 570: 563: 547: 542: 527: 508: 504: 489: 453: 449: 426: 403: 399: 362: 358: 317: 313: 302:, pp. 405-460. 294: 290: 286: 240:Poisson bracket 167: 111:Quantum physics 92: 88: 77: 68: 63: 61: 53: 44: 38: 36: 35: 34: 24: 17: 12: 11: 5: 754: 744: 743: 738: 733: 728: 723: 718: 713: 708: 703: 698: 682: 681: 674: 667: 659: 656: 655: 642: 629: 628: 621: 614: 606: 603: 602: 589: 561: 560: 554: 546: 545:External links 543: 541: 540: 525: 502: 487: 447: 424: 397: 356: 311: 287: 285: 282: 195:LĂ©on Rosenfeld 166: 163: 130: 129: 126: 125: 123:LĂ©on Rosenfeld 120: 114: 113: 108: 104: 103: 97: 96: 83: 82:Known for 79: 78: 69: 66:(aged 86) 59: 55: 54: 45: 32: 30: 26: 25: 22: 15: 9: 6: 4: 3: 2: 753: 742: 739: 737: 734: 732: 729: 727: 724: 722: 719: 717: 714: 712: 709: 707: 704: 702: 699: 697: 694: 693: 691: 680: 675: 673: 668: 666: 661: 660: 654: 652: 648: 643: 640: 636: 635: 627: 622: 620: 615: 613: 608: 607: 601: 599: 595: 590: 587: 580: 574: 569: 568: 564: 558: 555: 552: 549: 548: 536: 532: 528: 526:9781526600196 522: 518: 517: 512: 506: 498: 494: 490: 484: 480: 476: 472: 468: 464: 459: 451: 443: 439: 435: 431: 427: 425:9781461471158 421: 417: 413: 409: 401: 392: 387: 383: 379: 375: 371: 367: 360: 352: 348: 344: 340: 335: 330: 326: 322: 315: 309: 305: 301: 298: 292: 288: 280: 276: 274: 270: 269: 264: 259: 257: 253: 251: 245: 241: 237: 233: 230: 226: 225:Moyal bracket 221: 219: 215: 211: 207: 202: 200: 196: 192: 188: 187:Frits Zernike 184: 180: 176: 172: 162: 160: 156: 152: 148: 144: 140: 136: 127: 124: 121: 119: 115: 112: 109: 105: 102: 98: 95: 91: 87: 84: 80: 76: 72: 60: 56: 52: 48: 31: 27: 20: 651:expanding it 644: 598:expanding it 591: 562: 514: 505: 462: 450: 407: 400: 373: 369: 359: 324: 320: 314: 299: 296: 291: 278: 266: 261:Philosopher 260: 247: 235: 222: 218:star-product 203: 168: 142: 138: 134: 133: 100: 64:(1996-11-23) 43:29 July 1910 701:1996 deaths 696:1910 births 469:. pp.  248:Groenewold– 210:J. E. Moyal 155:phase space 75:Netherlands 51:Netherlands 690:Categories 535:1143365836 488:902770158X 284:References 244:Paul Dirac 232:commutator 143:Groenewold 39:1910-07-29 511:Ord, Toby 467:D. Reidel 442:117837329 434:828487961 351:119230734 334:1104.5269 327:: 37–46. 175:Groningen 171:Muntendam 165:Biography 157:known as 71:Groningen 47:Muntendam 513:(2020). 263:Toby Ord 250:Van Hove 471:359–366 378:Bibcode 297:Physica 252:theorem 238:to the 229:quantum 191:De Bilt 533:  523:  497:111732 495:  485:  440:  432:  422:  349:  254:. See 107:Fields 438:S2CID 347:S2CID 329:arXiv 647:stub 594:stub 531:OCLC 521:ISBN 493:OCLC 483:ISBN 430:OCLC 420:ISBN 58:Died 29:Born 475:doi 412:doi 386:doi 374:109 339:doi 304:doi 197:at 153:in 139:Hip 692:: 529:. 491:. 481:. 473:. 436:. 428:. 418:. 384:. 372:. 368:. 345:. 337:. 325:01 323:. 300:12 161:. 141:" 73:, 49:, 678:e 671:t 664:v 653:. 625:e 618:t 611:v 600:. 537:. 499:. 477:: 444:. 414:: 394:. 388:: 380:: 353:. 341:: 331:: 306:: 137:" 41:) 37:(

Index

Muntendam
Netherlands
Groningen
Netherlands
Groenewold's theorem
Weyl–Groenewold product
Phase-space formulation
Quantum physics
Doctoral advisor
LĂ©on Rosenfeld
theoretical physicist
quantum mechanics
phase space
phase-space quantization
Muntendam
Groningen
University of Groningen
John von Neumann
Frits Zernike
De Bilt
LĂ©on Rosenfeld
Utrecht University
quantum mechanics in phase space
J. E. Moyal
Wigner–Weyl transform
star-product
Moyal bracket
quantum
commutator
Poisson bracket

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