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 the path of the particle or centre of mass of the rigid body passes through the given origin, its angular momentum is zero.

If we define r < sub > i </ sub > as the displacement of particle i from the center of mass, and v < sub > i </ sub > as the velocity of particle i with respect to the center of mass, then we have

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

If we think of the atoms as impenetrable steel discs and the impinging particle as a bullet of negligible diameter, this ratio is the probability that the bullet will strike a steel disc, i. e., that the atomic projectile will be stopped by the foil.

If this acceleration is multiplied by the particle mass, the leading term is the centripetal force and the negative of the second term related to angular acceleration is sometimes called the Euler force.

If the depletion layer is large enough to catch the whole shower or to stop a heavy particle, a fairly accurate measurement of the particle ’ s energy can be made, simply by measuring the charge conducted and without the complexity of a magnetic spectrometer, etc.

If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which all other particles are made.

If the entire volume of the observable universe ( taken to be 3 × 10 < sup > 80 </ sup > m < sup > 3 </ sup >) were packed solid with fine dust particles about 1. 5 micrometres in size, then the number of different ways of ordering these particles ( that is, assigning the number 1 to one particle, then the number 2 to another particle, and so on until all particles are numbered ) would be approximately one googolplex.

If the particles are indistinguishable, this is impossible by definition ; either particle can be in either state.

If the particles are bosons, they occupy a totally symmetric state, which is symmetric under the exchange of any two particle labels:

If a particle of charge q moves with velocity v in the presence of an electric field E and a magnetic field B, then it will experience a force

If a force is applied to a particle for a time interval, the momentum of the particle changes by an amount

If the particle is moving at speed in the first frame of reference, in the second it is moving at speed

If a charged particle moves in an electromagnetic field, its kinematic momentum is not conserved.

If, e. g., u is the speed of a particle, then the straightforward notation for its velocity is u, < u > u </ u >, or.

If the photon energy is absorbed, some of the energy liberates the electron from the atom, and the rest contributes to the electron's kinetic energy as a free particle.

If the spin of a particle has a positive projection on its direction of motion then it is called left-handed ; otherwise, it is right-handed.

If Alice has a particle which is entangled with a particle owned by Bob, and Bob teleports it to Carol, then afterwards, Alice's particle is entangled with Carol's.

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 the k < sup > th </ sup > single-particle energy eigenstate has energy and there are bosons in this state, then the total energy of these bosons is.

If this is so, then it does not have a single associated measurement as the system is not in an eigenstate of the observable.

If the unperturbed system is in eigenstate at time, its state at subsequent times varies only by a phase ( we are following the Schrödinger picture, where state vectors evolve in time and operators are constant ):

If the system is made up with a single particle in momentum eigenstate, then

If the system starts in an eigenstate of the initial Hamiltonian, it will end in the corresponding eigenstate of the final Hamiltonian.

If is increased adiabatically then the system at time will be in an instantaneous eigenstate of the current Hamiltonian, corresponding to the initial eigenstate of.

If an atom is initially in state in zero magnetic field ( on the red curve, at the extreme left ), an adiabatic increase in magnetic field will ensure the system remains in an eigenstate of the Hamiltonian throughout the process ( follows the red curve ).

If a system i-th energy eigenstate has n < sub > i </ sub > number of particles, the corresponding observable, the number operator, is given by

* If P = 0, then a non-degenerate eigenstate of H is also an eigenstate of the parity operator ; i. e., a non-degenerate eigenfunction of H is either invariant to P or is changed in sign by P.

If is an eigenstate with respect to an operator, then for the corresponding eigenvalue, and hence letting an operator act on is analogous to multiplying by the value of the classical variable to which corresponds.

If a Stokes beam is simultaneously present along with the pump, the virtual state can be used as an instantaneous gateway to address a vibrational eigenstate of the molecule.