Then, again, the conditional wave function of subsystem ( I ) is ( up to an irrelevant scalar factor ) equal to and if the Hamiltonian does not contain an interaction term between subsystems ( I ) and ( II ), satisfies a Schrödinger equation.

Then given the Hamiltonian operator, the equation to satisfy for all functions ( with associated multiplication operator ) is

Then when the high energy degrees of freedoms are integrated out, the effective Hamiltonian in the low energy subspace reads

Then, the first order correction to the Hamiltonian is

Then having found the weight of the shortest Hamilton path, determine which edges are in the path by asking for each edge whether there is a Hamiltonian path with weight for the graph modified so that edge has weight ( if there is no such path in the modified graph, then edge must be in the shortest path for the original graph ).

Then the total Hamiltonian of the ensemble is

Then, the Z < sub > 2 </ sub > parity of the number of χ particles is well defined and is conserved in time ( even though the number of χ particles itself depends on the choice of which splitting into a free Hamiltonian and an interacting Hamiltonian we make in the interaction picture, which doesn't even exist for interacting theories ( the number is typically infinite )).

Then, to find the expectation value of the Hamiltonian:

Then the Hamiltonian vector field with Hamiltonian H takes the form

Then a curve γ ( t )=( q ( t ), p ( t )) is an integral curve of the Hamiltonian vector field X < sub > H </ sub > if and only if it is a solution of the Hamilton's equations:

Then one says that the symmetry of the Hamiltonian is realized by the system.

Then the unperturbed Hamiltonian of the atom can be written as

Then under the dipole approximation the interaction Hamiltonian between the atom and the electric field can be expressed as

Then Little Billy began shouting orders to round up the ponies and fill the water buckets and for the cooks to hurry up with the meal.

Then, helpfully, as she merely stared at him in weary silence, `` Maybe you could write it down for me, huh??

Then they were tumbling again, and the big man reached into the same pocket he had gone for earlier, and came up with a vicious switchblade.

`` Then I return to the United States for engagements at the Hollywood Bowl and in Philadelphia '', he added.

Then Miriam varied the senseless psychological warfare by suddenly withdrawing a suit for separate maintenance that had been pending, and asking for divorce on the grounds of cruelty, with the understanding that Wright would not contest it.

My own stern hand has rent the ancient bond, And thereof shall the ending not have end: But not for me, that loved her, to be fond Lightly to please me with a newer friend Then hold it more than bravest-feathered song, That I affirm to thee, with heart of pride, I knew not what did to a friend belong Till I stood up, true friend, by thy true side ; ;

Then Meltzer's voice, quiet, calm, strong, started the Kaddish, the prayer for the dead.

Then they returned to their hotel and got ready for bed.

Then he kept Blackman awake for more than an hour while he did an imaginary dialogue between his wife and himself in which, discussing the evening, he was continually berated.

Then we have surviving at least one instance of a poem prepared for another, in Naturam non Pati Senium, and perhaps also the De Idea Platonica.

Then followed a period in which he wrote reviews for The New York Times Book Review, The Commonweal, Commentary, had a small piece in Partisan Review, and moved on to Hudson, The Village Voice, and Exodus.

Then a full-time planning office will be established in Rome to work with a five-member Georgia Tech research staff for development of an area planning and industrial development program.

Then Goodbody will hand over a minimum of $15.5 million for developing the spacious Graves Tract to house the center.

Then, to conclude on an indeterminate note: `` Nevertheless, if fallout increased substantially, or remained high for a long time, it would become far more important as a potential health hazard in this country and throughout the world ''.

Then, abandoning the studies in the face of their promising outlook for all concerned, B. & O. entered on-again-off-again negotiations with C. & O. which resulted in the present situation.

Then they were given 1/2 to 1-1/2 avocados per day as a substitute for part of their dietary fat consumption.

Then, after emasculation, he was eased up for a couple of weeks.

Then you'll want terry cloth towels for mopping up.

Then, for the above parasites, feed continuously at these levels: Feeder cattle -- 2-5 grams of phenothiazine daily ; ;

Then, too, European drivers have reputations for being somewhat crazy on the road and some Americans are not particularly keen on getting mixed up with them.

Then, for the first time since his arrest, a glint of spirit lit Barco's eyes.

Then, I remembered that the girls had had a banana for dessert every day for the last week.

Then, having wrapped the lot in an afghan my dog customarily slept on, you lammed out the front door, considerately leaving it open for neighbors to discover.

Then, one will notice that there are two columns of delays () that tap off the center net, and these can be combined since they are redundant, yielding the implementation as shown below.

Then in 1817, in turn, a portion of Seneca County was combined with a piece of the remainder of Cayuga County to form Tompkins County.

Then Disney consultant and children's book author Robert D. San Souci suggested making a movie of the Chinese poem, " The Song of Fa Mu Lan " and Disney combined the two separate projects.

Then in 1817, in turn, a portion of Seneca County was combined with a piece of the remainder of Cayuga County to form Tompkins County.

Then, the two elementary schools to Grade 8 were combined.

Then, after just three days in the mining camp, he accepted the nomination to run for alcalde, a Mexican official, which combined the duties of a mayor and justice of the peace, in a new government that was being formed.

Then, combined with the wage Phillips curve 1 and the assumption made above about the trend behavior of money wages 2, this price-inflation equation gives us a simple expectations-augmented price Phillips curve:

Then all the parties which resented the limit upon freedom of election combined in Paris to rise in revolt.

Then in 1946, the YPWW Department was combined with the Sunday School Department for joint conventions until 1951 when they were separated once again.

Then United Nations Secretary-General Kofi Annan commented that " he combined respect for humankind with concern for our environment.

Then, the individual normal equation matrices were combined and the resultant matrix solved to obtain the positions and the parameters.

Then the other tree become a subtree of the combined tree.

Then the two terms which contain time derivatives can be combined into a single term.

Then on October 12, 1903, Act No. 942 combined Pateros, Taguig and Muntinlupa into a single municipality under Pateros.

Then, in 1537, it combined with the Salt Fishmongers ' Company to form the Company of the present name.

Then Lord Shiva grants her wish saying that she would get the same in her next birth with five husbands, she was shocked and asked lord shiva is it a boon or curse, shiva replied back saying " My child do not get worried, you will regain your virginity each an every morning you take bath, till the end of your life you will live with virginity " Hence she gets married to brothers each who represents a given quality: The just Yudhisthira for his wisdom of Dharma ; The powerful Bhima for his strength that exceeded that of a thousand elephants combined ; The valiant Arjuna for his courage and knowledge of the battlefield ; the exceedingly handsome Nakula and Sahadeva, for their love.

Then the sea and the river combined in about 1375 to destroy the eastern part of the town and ships began use the current area ( the Strand ) to unload their cargoes.

Then in 1993 Ameritech and Bell Atlantic reduced their share in Telecom to a combined 49. 6 %, and BellSouth ( now Vodafone ) set up the first mobile network to compete with Telecom.

Then the loose sheets are combined into small units or signatures, which are secured with overlock stitching.

Then combined with his own funds to subsidize the construction of a university campus.

In 1953, portions of 613 and 416 were combined to form area code 519 in Southwestern Ontario ; Then, in 1957, the Northern parts of 613 ( along with a small section of 519 ) became the 705 area code, leaving 613 covering only Eastern Ontario.

Then the terms involving in can be combined as

Then from 1974 – 1981 the race was run on the " No. 15 " configuration, the longest and fastest configuration, a section that combined 2 very fast successive right and left hand corners with 2 long straights and a spectacularly long and wide third corner ( called the Curvon Salotto ) combined with the infield section from the previous " No. 9 " configuration.