If a particle and antiparticle are in the appropriate quantum states, then they can annihilate each other and produce other particles.

If denotes the quantum state of a particle ( n ) with momentum p, spin J whose component in the z-direction is σ, then one has

If a suitably sized quantum computer capable of running Grover's algorithm reliably becomes available, it would reduce a 128-bit key down to 64-bit security, roughly a DES equivalent.

If the quantum state is initially symmetric ( antisymmetric ), it will remain symmetric ( antisymmetric ) as the system evolves.

If S contains two elements that are not pairwise orthogonal ( in particular, the set of all quantum states includes such pairs ) then an argument like that given above shows that the answer is no.

If the error rate is small enough, it is thought to be possible to use quantum error correction, which corrects errors due to decoherence, thereby allowing the total calculation time to be longer than the decoherence time.

If the theory of quantum gravity also achieves a grand unification of the other known interactions, it is referred to as a theory of everything ( TOE ).

If one used Planck's energy quanta, and demanded that electromagnetic radiation at a given frequency could only transfer energy to matter in integer multiples of an energy quantum hν, then the photoelectric effect could be explained very simply.

If certain quantum inequalities conjectured by Ford and Roman hold, then the energy requirements for some warp drives may be absurdly gigantic as well as negative, for example the energy equivalent of − 10 < sup > 64 </ sup > kg might be required to transport a small spaceship across the Milky Way galaxy.

If the universe is described by an effective local quantum field theory down to the Planck scale, then we would expect a cosmological constant of the order of.

:" If the essential frequency range is limited to B cycles per second, 2B was given by Nyquist as the maximum number of code elements per second that could be unambiguously resolved, assuming the peak interference is less half a quantum step.

If a quantum computer with a sufficient number of qubits were to be constructed, Shor's algorithm could be used to break public-key cryptography schemes such as the widely used RSA scheme.

If true, sonoluminescence may be the first observable example of quantum vacuum radiation.

If more than one quantum mechanical state is at the same energy, the energy levels are " degenerate ".

If quantum mechanics were to be applicable to macroscopic objects, there must be some limit in which quantum mechanics reduces to classical mechanics.

If the effects of the quantum mechanical nuclear motion are to be studied, for instance because a vibrational spectrum is required, this electronic computation must be in nuclear coordinates.

If a more general measurement is made that detects the system in a state then the system makes a " jump " or quantum leap from the original state to the final state with probability of.

If the factor i were absent, the H matrix would be antihermitian and would have purely imaginary eigenvalues, which is not the traditional way quantum mechanics represents observable quantities like the energy.

If the middle layer is made thin enough, it acts as a quantum well.

If parity transforms a pair of quantum states into each other, then the sum and difference of these two basis states are states of good parity.

If we allow the elements of the system to use quantum computation, the system is called a quantum interactive proof system, and the corresponding complexity class is called QIP.

If we introduce a vector then each quantum state corresponds to a point in ' n-space ' with energy

If a lepton-antilepton pair is created, this process involves only quantum electrodynamics ( QED ), but if a quark-antiquark pair is created, it involves both QED and perturbative quantum chromodynamics ( QCD ).

If you were a man '' --

If she, Pamela, were being held responsible for his crimes, then hers must be the final act of expiation.

If someone were to drop a match in here, this place would go up like a haystack ''.

If the other pilots were worried, they did not show it.

If it were the enemy, tactically his position was correct.

If it were not for an old professor who made me read the classics I would have been stymied on what to do, and now I understand why they are classics ; ;

If it were not that I knew who it was I could have mistaken it for my Aunt so well did her clothes fit him.

If an automobile were approaching him, he would know what was required of him, even though he might not be able to act quickly enough.

If there were only darkness, all would be clear.

If there were only the mess, all would be clear ; ;

If these people were denied a voice ( do they have a moral right to a voice??

If we were creating a wholly new society, we could insist that our social, political, economic and philosophic institutions foster rather than hamper man ; ;

If living Jews were unavailable for study, the Bible was at hand.

If his scholarship and formal musicianship were not all they might have been, Mercer demonstrated at an early age that he was gifted with a remarkable ear for rhythm and dialect.

If she were not at home, Mama would see to it that a fresh white rose was there.

If the Stearns were not there, grace would be omitted.

If anything, the conservative Democrats were more opposed to Hearst than the Republicans.

If the hardships of the winter at Valley Forge were trying for healthy men, they were, of course, much more so for those not in good health.

If his circumspection in regard to Philip's sensibilities went so far that he even refused to grant a dispensation for the marriage of Amadee's daughter, Agnes, to the son of the dauphin of Vienne -- a truly peacemaking move according to thirteenth-century ideas, for Savoy and Dauphine were as usual fighting on opposite sides -- for fear that he might seem to be favoring the anti-French coalition, he would certainly never take the far more drastic step of ordering the return of Gascony to Edward, even though, as he admitted to the English ambassadors, he had been advised that the original cession was invalid.

If there were no West Berlin problem, imperialist quarters would have invented an excuse for stepping up the armaments race to try to solve the internal and external problems besetting the United States and its NATO partners.

If the new Soviet series has followed the general pattern of previous Russian tests, the shots were roughly half fission and half fusion, meaning a fission yield of 30 to 40 megatons thus far.

If the Hessian troops sent here willy-nilly by the Hessian Government to fight for England in the 1770's were mercenaries, what shall we call the UN troops sent to the Congo willy-nilly by their governments to fight for the United Nations??

If the UN troops are not mercenaries then the Hessians were not mercenaries either.

If he were to go with White, he would be out there two days, not just listening in the dark at some point between here and Papa-san, but moving ever deeper into enemy land -- behind Papa-san -- itself.