If the wave function is regarded as ontologically real, and collapse is entirely rejected, a many worlds theory results.

If wave function collapse is regarded as ontologically real as well, an objective collapse theory is obtained.

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 a ray tracing is then made as if a light wave ( as understood in classical physics ) is wide enough to take both paths, then that ray tracing will accurately predict the appearance of maxima and minima on the detector screen when many particles pass through the apparatus and gradually " paint " the expected interference pattern.

If a crest of a wave meets a crest of another wave of the same frequency at the same point, then the magnitude of the displacement is the sum of the individual magnitudes – this is constructive interference.

If a crest of one wave meets a trough of another wave then the magnitude of the displacements is equal to the difference in the individual magnitudes – this is known as destructive interference.

* If the molecule has some symmetry, the degenerate atomic orbitals ( with the same atomic energy ) are grouped in linear combinations ( called symmetry-adapted atomic orbitals ( SO )), which belong to the representation of the symmetry group, so the wave functions that describe the group are known as symmetry-adapted linear combinations ( SALC ).

* If a storm or wave capsizes a small monohull, it may recover when the weight of the ballast in the keel rights the boat, if it does not broach and sink before it recovers.

If the pump waves and the signal wave are superimposed in a medium with a non-zero χ < sup >( 3 )</ sup >, this produces a nonlinear polarization field:

If two waves of the same wavelength and frequency are in phase, both the wave crests and wave troughs align.

If E < sub > i </ sub > is a sine wave, triangular wave, or wave of any other shape that is symmetrical around zero, the zero-crossing detector's output will be square.

If one knows the corresponding wave function at the instant before the measurement, one will be able to compute the probability of the wavefunction collapsing into each of the possible eigenstates.

If the wavelength is much shorter than the target's size, the wave will bounce off in a way similar to the way light is reflected by a mirror.

If an electron of energy E is incident upon an energy barrier of height U ( z ), the electron wave function is a traveling wave solution,

If a plane wave, confined to the xz plane, is incident on a dielectric with an angle and wavevector then a transmitted ray will be created with a corresponding angle of transmittance as shown in Fig.

If the first part of a tsunami to reach land is a trough — called a drawback — rather than a wave crest, the water along the shoreline recedes dramatically, exposing normally submerged areas.

If a traveling wave has a fixed shape that repeats in space or in time, it is a periodic wave.

If all the parts making up a medium were rigidly bound, then they would all vibrate as one, with no delay in the transmission of the vibration and therefore no wave motion.

If Af is the change per unit volume in Gibbs function caused by the shear field at constant P and T, and **yr is the density of the fluid, then the total potential energy of the system above the reference height is Af.

If a union cannot perform this function, then collective bargaining is being palmed off by organizers as a gigantic fraud.

If the Greek letter is used, it is assumed to be a Fourier transform of another function,

If the method is applied to an infinite sequence ( X < sub > i </ sub >: i ∈ ω ) of nonempty sets, a function is obtained at each finite stage, but there is no stage at which a choice function for the entire family is constructed, and no " limiting " choice function can be constructed, in general, in ZF without the axiom of choice.

If we try to choose an element from each set, then, because X is infinite, our choice procedure will never come to an end, and consequently, we will never be able to produce a choice function for all of X.

If the function R is well-defined, its value must lie in the range, with 1 indicating perfect correlation and − 1 indicating perfect anti-correlation.

If F is an antiderivative of f, and the function f is defined on some interval, then every other antiderivative G of f differs from F by a constant: there exists a number C such that G ( x ) = F ( x ) + C for all x.

If we define the function f ( n ) = A ( n, n ), which increases both m and n at the same time, we have a function of one variable that dwarfs every primitive recursive function, including very fast-growing functions such as the exponential function, the factorial function, multi-and superfactorial functions, and even functions defined using Knuth's up-arrow notation ( except when the indexed up-arrow is used ).

If f is not a function, but is instead a partial function, it is called a partial operation.

The tensor product X ⊗ Y from X and Y is a K-vector space Z with a bilinear function T: X × Y → Z which has the following universal property: If T ′: X × Y → Z ′ is any bilinear function into a K-vector space Z ′, then only one linear function f: Z → Z ′ with exists.

If your side has two aces and a void, then you are not at risk of losing the first two tricks, so long as ( a ) your void is useful ( i. e., does not duplicate the function of an ace that your side holds ) and ( b ) you are not vulnerable to the loss of the first two tricks in the fourth suit ( because, for instance, one of the partnership hands holds a singleton in that suit or the protected king, giving your side second round control ).

If evolutionary processes are blind to the difference between function F being performed by conscious organism O and non-conscious organism O *, it is unclear what adaptive advantage consciousness could provide.

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 it could be shown that judgments of good and bad were not judgments at all, that they asserted nothing true or false, but merely expressed emotions like `` Hurrah '' or `` Fiddlesticks '', then these wayward judgments would cease from troubling and weary heads could be at rest.

If, as a home movie maker, you shoot the inevitable footage of your child taking its first steps, you have merely recorded an historical event.

If laborers are merely commodities competing against each other in a market place like so many bags of wheat and corn ( unsupported, by the way, by any agricultural subsidy ), then they may be pardoned for reacting with complete antagonism to a system that imposes such status upon them.

If I wanted to be frivolous, I might say that everything that precedes editing is merely a way of producing film to edit.

If the executor is merely following a solution ( e. g. sketch, script or instructions ) provided by another designer ( such as an art director ), then the executor is not usually considered the designer.

If this is not due to chronological confusion of the events of the siege, it may suggest that Kallinikos merely introduced an improved version of an established weapon.

If unskilled labourers had it in their power to compete with skilled, by merely taking the trouble of learning the trade, the difference of wages might not exceed what would compensate them for that trouble, at the ordinary rate at which labour is remunerated.

If no additional energy is supplied by any other mechanism, the nucleus will not fission, but will merely absorb the neutron, as happens when U-238 absorbs slow and even some fraction of fast neutrons, to become U-239.

" If an interest is not deemed a " property " right, or the conduct is merely an intentional tort, these limitations do not apply and the doctrine of sovereign immunity precludes relief.

If one now shines a very intense beam of low-frequency light upon the same metal, a whole slew of electrons are ejected ; however they possess the same low energy, there are merely more of them.

If a set is well-ordered ( or even if it merely admits a wellfounded relation ), the proof technique of transfinite induction can be used to prove that a given statement is true for all elements of the set.

If so, all I can say is, it is a new Liberalism, and not the one that I have known and practised under more illustrious auspices than these, under one who was not merely the greatest Liberal but the greatest financier that this country has ever known — I mean Mr. Gladstone ... Gladstone ranks as the great financial authority of our country ... Mr. Gladstone would be 100 in December if he were alive, but, centenarian as he would be, I am inclined to think that he would make very short work of the deputation of the Cabinet that waited on him with this measure, and that they would soon find themselves on the stairs, if not in the street.

He concluded that " If Marshall were merely stupid, the laws of probability would dictate that part of his decisions would serve this country's interest.

If the action can only result in a simple success or failure, the die roll of 1-10 is merely added to the total ( called a " Simple roll ").

In fact, this process is merely a fancier form of the classic Liar ParadoxA: If I say, " I am a liar ", then how can it be true if I am telling the truth therewith, and, if I am telling the truth therewith, then how can I be a liar?

If the defendant was selected from a large group merely because of the evidence under consideration, then this fact should be included in weighing how incriminating that evidence is.

If one spoke in the lingua or sermo Latinus one merely spoke Latin, but if one spoke latine or latinius (" more Latinish ") one spoke good Latin, and formal Latin had latinitas, the quality of good Latin, about it.

If it had not been for George W. O ' Brien, the place which was to become Wickett might have remained as Aroya, merely a switch and a section house on the Texas and Pacific Railroad, established to house one of the maintenance crews for the railroad.

If Harold was not properly crowned, then William was merely claiming his rightful inheritance, and not deposing a rightful king.

If the Queen bears no sons, she is merely a foreigner in the State, and a very dangerous foreigner, too.

If there are slack resources, we need merely mobilize some of the slack resources.

He wrote, " Mr. David Stockman has said that supply-side economics was merely a cover for the trickle-down approach to economic policy — what an older and less elegant generation called the horse-and-sparrow theory: If you feed the horse enough oats, some will pass through to the road for the sparrows.

" If one believes that the trust fund assets are worthless ," argued former Representative Bill Archer, then similar reasoning implies that “ Americans who have bought EE savings bonds should go home and burn them because they ’ re worthless because the money has already been spent .” At a Senate hearing in July 2001, Federal Reserve Chairman Alan Greenspan was asked whether the trust fund investments are “ real ” or merely an accounting device.

If there was a riding surrounding the wapentake, the wapentake would merely be a local assembly coordinating the power of the Riding, which in Jorvik's case, would be under the king's command at what is now King's Square in York.