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

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 the glass is damaged, atmospheric pressure can collapse the vacuum tube into dangerous fragments which accelerate inward and then spray at high speed in all directions.

If the core becomes sufficiently dense, electron degeneracy pressure will play a significant part in stabilizing it against gravitational collapse.

If a reaction results in a small energy release making way for more energy releases in an expanding chain, then the system will typically collapse explosively until much or all of the stored energy has been released.

If it does, it will develop into a red giant as described for mid-sized stars below, but never fuse helium as they do ; otherwise, it will simply contract until electron degeneracy pressure halts its collapse, becoming first a blue dwarf and then a white dwarf.

If the mass of the core exceeds the Chandrasekhar limit, electron degeneracy pressure will be unable to support its weight against the force of gravity, and the core will undergo sudden, catastrophic collapse to form a neutron star or ( in the case of cores that exceed the Tolman-Oppenheimer-Volkoff limit ), a black hole.

" If Psycho began an exploration of a new sense of absurdity in contemporary life, of the collapse of causality and the diseased underbelly of American Gothic ", he writes, The Texas Chain Saw Massacre " carries this exploration to a logical conclusion, addressing many of the issues of Hitchcock's film while refusing comforting closure ".

If a cloud is massive enough that the gas pressure is insufficient to support it, the cloud will undergo gravitational collapse.

If the volume of air is significant, one or both lungs may collapse, which requires immediate medical attention.

If the wave function merely encodes an observer's knowledge of the universe then the wave function collapse corresponds to the receipt of new information.

If the wave function is physically real, in some sense and to some extent, then the collapse of the wave function is also seen as a real process, to the same extent.

If caving stops and removal of ore from the drawbells continues, a large void may form, resulting in the potential for a sudden and massive collapse and potentially catastrophic windblast throughout the mine.

If we choose larger, then the four solutions will collapse to zero in terms of and they will become degenerate with the solution we found above.

If so, it apparently had not been sufficiently marked as a hospital ship, perhaps owing to the chaos surrounding the collapse of military and civilian authority in Nazi Germany.

If the area is further reduced once the solid phase has been reached, collapse occurs, the monolayer breaks and soluble aggregates and multilayers are formed

If their combined mass exceeds the Oppenheimer-Volkoff limit then the two will collapse into a black hole, resulting in a supernova that disperses the outer layers of the star.

If the roof of these voids becomes too weak, it can collapse and the overlying rock and earth will fall into the space, causing subsidence at the surface.

If such a collapse did occur, we could deduce that P ≠ PSPACE, since it is a well-known theorem that DTIME ( f ( n )) is strictly contained in DSPACE ( f ( n )).

If we add to this terror the blissful ecstasy that wells from the innermost depths of man, indeed of nature, at this collapse of the principium individuationis, we steal a glimpse into the nature of the Dionysian, which is brought home to us most intimately by the analogy of intoxication.

If the density of the universe is greater than the critical density, then the strength of the gravitational force will stop the universe from expanding and the universe will collapse back on itself.

If I ’ m persuaded that our life is predicated upon violence, that the entire structure of what we call civilization, the scaffolding that we ’ ve built up over the millennia, can collapse at any moment, then whatever I write is going to be affected by that assumption.

If the disturbance is sufficiently large, it may lead to gravitational instability and subsequent collapse of a particular region of the cloud.

If it is not eradicated, it will lead to social disintegration and societal collapse.