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 the medication is mixed with formulas containing iron or soya products, larger doses may be required, as these substances may alter the absorption of thyroid hormone from the gut.

If the earlier completion procedure is applied to a normed vector space, the result is a Banach space containing the original space as a dense subspace, and if it is applied to an inner product space, the result is a Hilbert space containing the original space as a dense subspace.

If the incident light is unpolarised ( containing an equal mix of s-and p-polarisations ), the reflection coefficient is

If a player's piece lands on a square containing an opponent's piece, the opponent's piece is captured and returns to the starting area.

If foods containing tryptophan are consumed, hyperserotonemia may result.

If they do not designate a new ruler after three days, then they open a letter left to them by the deceased Sultan, containing a recommendation for a new Sultan.

If the volcano rests on sediments containing mechanically weak layers ( e. g., beds of water-saturated clay ), detachment zones ( decollements ) may develop in the weak layers.

If organic or inorganic contaminations are present on the wafer surface, they are usually removed by wet chemical treatment, e. g. the RCA clean procedure based on solutions containing hydrogen peroxide.

If it is carried as packetized data over the Internet, anyone able to watch the packets containing the logon information can snoop with a very low probability of detection.

If values are stored by reference, e. g. objects, null references can be used and so the cluster can be represented by a vector containing 3 slots for value pointers plus 4 slots for child references in the tree.

If one measures by arc length one finds that the shortest path connecting two points lying entirely in the sphere is a segment of the great circle containing the points ; see geodesic.

# If alkaline transfer methods are used, the DNA gel is placed into an alkaline solution ( typically containing sodium hydroxide ) to denature the double-stranded DNA.

# If N is a subset of X containing a neighbourhood of x, then N is a neighbourhood of x.

If the pages containing these pointers or the code that they invoke were pageable, interrupt-handling would become far more complex and time-consuming, particularly in the case of page fault interrupts.

If he was less effective than his father in containing the Norman lords ' propensity for rebellion and violence, through charisma, or political skills, he was forceful in overcoming the consequences.

If the convex hull of X is a closed set ( as happens, for instance, if X is a finite set or more generally a compact set ), then it is the intersection of all closed half-spaces containing X.

If the hardened carrier is buried under ground, to secure cables running between buildings for example, the carrier containing the cables is encased in concrete.

If one considers the flux of the electric field vector, E, for a tube near a point charge in the field the charge but not containing it with sides formed by lines tangent to the field, the flux for the sides is zero and there is an equal and opposite flux at both ends of the tube.

If a block / subgraph is not connected from the subgraph containing the entry block, that block is unreachable during any execution, and so is unreachable code ; it can be safely removed.

If you are measuring the weight of some water, and you have a cup containing the water on a weighing scale, you must subtract the weight of the cup itself from your measurement, if you want to know the true weight of only the water itself.

If a box containing hazardous material is moved around and shifted into different positions, it is still easy to recognize the symbol.

Consider a jar containing N lottery tickets numbered from 1 through N. If you pick a ticket randomly then you get positive integer n, with probability 1 / N if n ≤ N and with probability zero if n > N. This can be written

If R qualifies as a member of itself, it would contradict its own definition as a set containing all sets that are not members of themselves.

If the currency being withdrawn from the ATM is different from that which the bank account is denominated in ( e. g.: Withdrawing Japanese Yen from a bank account containing US Dollars ), the money will be converted at an official wholesale exchange rate.