William Rowan Hamilton - 2026 ACF Regionals

Question

A formulation developed by this physicist inspired the phase space formulation of quantum mechanics. For 10 points each:

[10m] Name this physicist whose principal function, S, is the action. This physicist’s formulation of classical mechanics is expressed in terms of generalized momenta.

ANSWER: William Rowan Hamilton [accept Hamilton’s principal function; accept Hamiltonian mechanics]

[10e] The negative derivative of Hamilton’s principal function with respect to this quantity gives the Hamiltonian. The derivative of position with respect to this quantity gives velocity.

ANSWER: time

[10h] For a system of N particles, this number times N gives the dimensionality of Hamiltonian phase space. This number is the number of independent components of the Cauchy (“ko-SHEE”) stress tensor.

ANSWER: six

<GC, Physics>

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Summary


California (North)	Main Site	Y	3	23.33	100%	33%	100%
California (South)	Main Site	Y	4	15.00	100%	50%	0%
Canada	Main Site	Y	11	11.82	73%	27%	18%
Florida	Main Site	Y	3	10.00	67%	0%	33%
Great Lakes	Main Site	Y	5	20.00	100%	60%	40%
Lower Mid-Atlantic	Main Site	Y	9	11.11	89%	22%	0%
Midwest	Main Site	Y	8	12.50	100%	25%	0%
Northeast	Main Site	Y	6	16.67	100%	50%	17%
Overflow	Main Site	Y	4	12.50	100%	0%	25%
South Central	Main Site	Y	2	10.00	100%	0%	0%
Southeast	Main Site	Y	8	15.00	88%	38%	25%
UK	Main Site	Y	12	14.17	100%	25%	17%
Upstate NY	Main Site	Y	4	10.00	100%	0%	0%

Data


Berkeley A	Berkeley C	0	10	10	20
UCLA B	UCSD B	10	10	0	20
UC Irvine	Arizona State	0	10	0	10
UCLA A	UC Santa Barbara	10	10	0	20
UCSD C	UCSD A	0	10	0	10
Brock	Toronto C	0	0	0	0
Carleton University	Simon Fraser	0	10	0	10
Guelph	Toronto F	0	10	0	10
Toronto E	Toronto G	10	10	0	20
Toronto Metropolitan	Toronto B	0	0	0	0
UBC A	Western C	0	10	0	10
Waterloo A	UBC B	10	10	10	30
Ottawa	McGill A	10	10	10	30
McGill B	Western A	0	10	0	10
McMaster B	Toronto D	0	0	0	0
Queen's	Western B	0	10	0	10
Central Florida A	Central Florida C	0	10	0	10
Central Florida B	Florida B	0	10	0	10
Florida C	Florida A	0	0	10	10
Virginia	Liberty A	10	10	0	20
Liberty B	South Carolina B	0	10	0	10
North Carolina A	James Madison B	0	10	0	10
South Carolina A	NC State B	0	10	0	10
VCU	NC State A	0	0	0	0
Virginia Tech A	Duke	10	10	0	20
Virginia Tech B	Liberty C	0	10	0	10
North Carolina B	Wake Forest	0	10	0	10
William and Mary	North Carolina C	0	10	0	10
Chicago B	Illinois C	0	10	0	10
Illinois B	Chicago D	0	10	0	10
Chicago A	Indiana A	0	10	0	10
Northwestern D	Indiana C	0	10	0	10
Chicago C	Northwestern C	0	10	0	10
Notre Dame A	Chicago E	10	10	0	20
Purdue A	Illinois A	0	10	0	10
Northwestern B	Purdue B	10	10	0	20
Bowdoin B	Bowdoin A	0	10	0	10
Brown	Brandeis A	10	10	10	30
Dartmouth A	Brandeis B	0	10	0	10
MIT	Dartmouth B	10	10	0	20
Harvard A	Harvard B	10	10	0	20
Yale	Southern Connecticut State	0	10	0	10
Georgia Tech A	Iowa State	0	10	0	10
Minnesota A	Carleton College	0	10	0	10
Missouri A	Missouri B	0	10	0	10
Washington A	Washington B	0	10	10	20
Texas A	Texas A&M A	0	10	0	10
Texas B	Murray State A	0	10	0	10
Michigan B	CWRU B	10	10	0	20
Michigan A	Michigan C	10	10	10	30
Michigan State	Ohio State B	0	10	0	10
Pittsburgh	Ohio State A	10	10	0	20
CWRU A	Ohio State C	0	10	10	20
Georgia Tech C	Alabama A	10	10	10	30
Louisville A	Alabama B	0	10	0	10
Bruin	Tennessee A	10	0	0	10
WashU A	Georgia Tech D	0	10	10	20
Edinburgh B	Birmingham	0	10	0	10
Warwick A	Bristol	0	10	0	10
Edinburgh A	Cambridge B	0	10	10	20
Southampton A	Durham	0	10	0	10
Imperial A	Manchester	0	10	0	10
Imperial B	UCL	10	10	0	20
Montpellier	LSE	0	10	0	10
Cambridge A	Oxford A	10	10	10	30
Oxford B	Cardiff	0	10	0	10
Imperial C	Oxford C	0	10	0	10
Southampton B	City St. George's	10	10	0	20
Warwick B	Cambridge C	0	10	0	10
Georgia Tech B	Louisville B	0	10	0	10
Kentucky	Tennessee B	10	10	0	20
Mississipi State	Vanderbilt B	0	10	0	10
Sewanee	WashU B	0	10	0	10
Cornell C	Binghamton B	0	10	0	10
Cornell A	Cornell B	0	10	0	10
Binghamton A	Penn State	0	10	0	10
RIT	Rochester	0	10	0	10
Stanford B	Berkeley D	10	10	10	30
Berkeley B	Stanford A	0	10	10	20