If we take the simple valence bond structure and mix in all possible covalent and ionic structures arising from a particular set of atomic orbitals, we reach what is called the full configuration interaction wave function.

If we take the simple molecular orbital description of the ground state and combine that function with the functions describing all possible excited states using unoccupied orbitals arising from the same set of atomic orbitals, we also reach the full configuration interaction wavefunction.

If a particle of the beam crosses this surface, there will be some kind of interaction.

If it is " observed " ( measured with a photon ) not at a particular slit but rather at the screen, then there is no " which path " information as part of the interaction, so the electron's " observed " position on the screen is determined strictly by its probability function.

If is a quaternion valued spinor, is quaternion hermitian 4x4 matrix coming from Sp ( 8 ) and is a pure imaginary quaternion ( both of which are 4-vector bosons ) then the interaction term is:

If the velocities of the particles are and before the interaction, and afterwards they are and, then

If the objects are indeterminate until one of them is measured, then the question becomes, " How can one account for something that was at one point indefinite with regard to its spin ( or whatever is in this case the subject of investigation ) suddenly becoming definite in that regard even though no physical interaction with the second object occurred, and, if the two objects are sufficiently far separated, could not even have had the time needed for such an interaction to proceed from the first to the second object?

If an end user interaction with dates and times is required, the software will nearly always convert this internal number into a date and time representation that is comprehensible to humans.

If the source document is subsequently modified, then those text units that have not changed can be directly transferred to the new target version of the document without the need for any translator interaction.

To promote the release of If Not Now, When ?, the band took part in a participatory media exhibit and real-time documentary called Incubus HQ Live that allowed unprecedented fan access and interaction.

If users accept the loss of two-way interaction, identity anonymity can be made more secure.

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

If a planet's magnetic field is strong enough, its interaction with the solar wind forms a magnetosphere.

If the containment fields ever fail, the subsequent interaction of the antimatter fuel with the container walls would result in a catastrophic release of energy, with the resultant explosion capable of utterly destroying the ship.

There exists a link between sudden stratospheric warmings and the quasi-biennial oscillation: If the QBO is in its easterly ( westward ) phase, the atmospheric waveguide is modified in such a way that upward-propagating Rossby waves are focused on the polar vortex, intensifying their interaction with the mean flow.

If the interaction term is small ( less than the fine structure ), it can be treated as a perturbation ; this is the Zeeman effect proper.

If the spin-orbit interaction dominates over the effect of the external magnetic field, and are not separately conserved, only the total angular momentum is.

If they are not, such as a proton and an electron, the interaction is different.

If we want to understand cause, focus on social interaction.

If a more precise solution is desired, another iteration is then performed, using the positions and motions of the planets as identified in the first iteration, but adding a first-order gravity interaction from each planet on the others.

If one expects real-time interaction with the distributed system, this may be very noticeable.

If the CVxIV interaction is significant, ANCOVA should not be performed.

If the CVxIV interaction is not significant, rerun the ANCOVA without the CVxIV interaction term.

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 Jews are identified as a religious body in a controversy that comes before a national or international tribunal, it is obviously compatible with the goal of human dignity to protect freedom of worship.

If world peace depended solely on financial support, it would not seem a goal, but more like an act of pity.

* If you want to be happy, set a goal that commands your thoughts, liberates your energy, and inspires your hopes.

If both extra periods are played without a scored goal, a penalty shootout will settle the game.

If a team fails to gain ten yards in two downs they usually punt the ball on third down or try to kick a field goal ( see below ), depending on their position on the field.

* If the offence scores a field goal, the scoring team must kickoff from their own 35-yard line.

If a kicked ball goes out of bounds, or the kicking team scores a single or field goal as a result of the kick, the other team likewise gets possession.

If the original penalty yardage would have resulted in a first down or moving the ball past the goal line, a first down is awarded.

If they make what would normally be a field goal, they score one point ; what would normally be a touchdown scores two points ( a " two-point conversion ").

If a group has an involution with a 2-component that is a group of Lie type of odd characteristic, the goal is to show that it has a centralizer of involution in " standard form " meaning that a centralizer of involution has a component that is of Lie type in odd characteristic and also has a centralizer of 2-rank 1.

If ultra-pure products are the goal, then further chemical separation must be applied.

If this goal is met by a DBMS, then the designers and builders of the specific database can concentrate on the application's aspects, and not deal with building and maintaining the underlying DBMS.

Ethical egoists such as Rand who readily acknowledge the ( conditional ) value of others to an individual, and who readily endorse empathy for others, have argued the exact reverse from Rachels, that it is altruism which discriminates: " If the sensation of eating a cake is a value, then why is it an immoral indulgence in your stomach, but a moral goal for you to achieve in the stomach of others?

If the ball is carried by a player, it is considered a score when any part of the ball is directly above or beyond any part of the goal line between the pylons.

If any member of the offensive team is downed while in possession of the ball behind his own team's goal line, this is called a safety and scores two points for the defensive team.

If, during the course of play, a loose ball travels past the goal line and is recovered within the end zone, then it is a touchdown if recovered by the team striving toward that goal, or a touchback if recovered and downed by the team striving toward the goal at the opposite end of the field.

If a player contacts the ground inside the goal perimeter he must take the most direct path out of it.

If the goalkeeper deflects the ball over the outer goal line, their team stays in possession of the ball in contrast to other sports like association football.

If they had ₤ 1000 in assets they could get a free ; the goal of the government was to speed up modernization and economic growth.

The goal of the defenders is to stop the raider from returning to the home side before taking a breath. If any of the seven players cross the lobby without touching the raider he will be declared as " out ".

If a definite statement is believed plausible by some mathematicians but has been neither proved nor disproved, it is called a conjecture, as opposed to an ultimate goal: a theorem that has been proved.

If a team does not attempt to score a field goal ( or the ball fails to make contact with the rim ) within 24 seconds of obtaining the ball, play is stopped and the ball given to its opponent.

If anything, the goal behind outing is to show just how many gay people there are among the most visible people in our society so that when someone outs the milkman or the spinster, everyone will say, ' So what?