If the Hamiltonian is time-independent,

If we have a Hamiltonian with a space representation, say

If we wish to maintain this interpretation on passing to the Dirac theory, we must take the Hamiltonian to be

If this fragment is part of a larger graph, then any Hamiltonian cycle through the graph must go in or out of the top vertex ( and either one of the lower ones ).

If, in addition, the Hamiltonian does not contain an interaction term between subsystems ( I ) and ( II ) then does satisfy a Schrödinger equation.

If the Hamiltonian is not an explicit function of time, the equation is separable into its spatial and temporal parts.

If such a Hamiltonian has a unique lowest energy state with a positive real wave-function, as it often does for physical reasons, it is connected to a stochastic system in imaginary time.

If the system is not in its ground state and the bath is at a temperature lower than that of the system's, then the system will give off energy to the bath and thus higher-energy eigenstates of the system Hamiltonian will decohere to the ground state after cooling and, as such, they will all be non-degenerate.

If G is a 2-connected, r-regular graph with at most 3r + 1 vertices, then G is Hamiltonian or G is the Petersen graph.

If we choose this trial Hamiltonian such that

If we write the Hamiltonian as:

If the Hamiltonian is independent of time, the solution to the above equation is:

If the Hamiltonian is dependent on time, but the Hamiltonians at different times commute, then the time evolution operator can be written as:

If the graph is a metric space then there is an efficient approximation algorithm that finds a Hamiltonian cycle with maximum edge weight being no more than twice the optimum.

* If Peggy is asked to prove that she knows a Hamiltonian cycle in H, she translates her Hamiltonian cycle in G onto H and only uncovers the edges on the Hamiltonian cycle.

If Peggy is honest, she can easily satisfy Victor's demand for either a graph isomorphism ( which she has ) or a Hamiltonian cycle ( which she can construct by applying the isomorphism to the cycle in G ).

If Peggy does not know of a Hamiltonian Cycle in G, but somehow knew in advance what Victor would ask to see each round then she could cheat.

If Peggy does not know the information, she can guess which question Victor will ask and generate either a graph isomorphic to G or a Hamiltonian cycle for an unrelated graph, but since she does not know a Hamiltonian cycle for G she cannot do both.

* If the Lagrangian is time-independent the Hamiltonian is also time-independent ( i .. e both are constant in time ).

If a degree of freedom x < sub > n </ sub > appears only as a quadratic term a < sub > n </ sub > x < sub > n </ sub >< sup > 2 </ sup > in the Hamiltonian H, then the first of these formulae implies that

* If a graph G has an Euler cycle, that is, if G is connected and has an even number of edges at each vertex, then the line graph of G is Hamiltonian.

If the circumstances are faced frankly it is not reasonable to expect this to be true.

If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.

If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.

If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;

If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.

If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.

If it is an honest feeling, then why should she not yield to it??

If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.

If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.

If he is good, he may not be legal ; ;

If the man on the sidewalk is surprised at this question, it has served as an exclamation.

If the existent form is to be retained new factors that reinforce it must be introduced into the situation.

If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??

If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.

If he is a traditionalist, he is an eclectic traditionalist.

If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.

If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.

* If the kinetic energy is a homogeneous function ( of degree 2-quadratic ) of the generalized velocities and the Lagrangian is explicitly time-independent:

If the Hamiltonian has explicit time-dependence ( for example, if the quantum system interacts with an applied external electric field that varies in time ), it will usually be advantageous to include the explicitly time-dependent terms with, leaving time-independent.

If is time-independent, the system goes only into those states in the continuum that have the same energy as the initial state.

Acetylcholine also inhibits the hyperpolarization-activated " pacemaker " current If the " Ik decay " hypothesis65 proposes that pacemaker depolarization results from slow deactivation of the delayed rectifier current, Ik, which, due to a time-independent background inward current, causes diastolic depolarization.