ladder operators - 2023 Penn Bowl

Question

These two operators are multiplied by hyperbolic trig functions in the Bogoliubov transformation. For 10 points each:

[10m] Identify this pair of operators, denoted “a” and “a-dagger”, which are used to increase or lower the quanta of energy of a state. These operators were introduced to solve the quantum harmonic oscillator.

ANSWER: ladder operators [accept creation and annihilation operators]

[10h] In the occupation number representation, the ladder operators add or remove particles for multi-particle states in this space, which is a direct sum of tensor products of single-particle Hilbert spaces.

ANSWER: Fock space

[10e] The potential energy of the classical harmonic oscillator is given by this law, which states it is equal to one-half times spring constant times displacement squared

ANSWER: Hooke’s law

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Summary


2023 Penn Bowl (Harvard)	10/21/2023	Y	3	13.33	100%	33%	0%
2023 Penn Bowl (Mainsite)	10/21/2023	Y	6	13.33	100%	33%	0%
2023 Penn Bowl @ Waterloo	10/28/2023	N	4	20.00	100%	75%	25%
2023 Penn Bowl @ FSU	10/28/2023	N	2	15.00	100%	50%	0%
2023 Penn Bowl (Norcal)	10/28/2023	N	2	30.00	100%	100%	100%
2023 Penn Bowl (South Central)	10/28/2023	N	3	13.33	67%	67%	0%
2023 Penn Bowl (UK)	10/28/2023	N	5	22.00	100%	80%	40%

Data


Brown	Boston College	10	10	20
Brandeis	MIT	0	10	10
Harvard	Tufts	0	10	10
Cornell A	Columbia B	0	10	10
Rutgers	JHU A	0	10	10
John Jay A	Swarthmore	10	10	20
NYU	Cornell B	0	10	10
Pitt	RIT	0	10	10
UMD A	JHU B	10	10	20