When calculating scattering cross sections in particle physics, the interaction between particles can be described by starting from a free field which describes the incoming and outgoing particles, and including an interaction Hamiltonian to describe how the particles deflect one another.

:: When the Hamiltonian operator acts on the wavefunction Ψ, the result might be proportional to the same wavefunction Ψ.

When the above hold, quantum theory can be extended to a Euclidean theory, defined by translating all the operators to imaginary time using the Hamiltonian.

When we put in the expression for the Hamiltonian we get:

When the final time is fixed and the Hamiltonian does not depend explicitly on time, then:

When a cubic graph is Hamiltonian, LCF notation allows it to be represented concisely.

This process has been studied first in a measurement situation: When the system is an apparatus whose intrinsic dynamics can be neglected, pointer states turn out to be eigenstates of the interaction Hamiltonian between the apparatus and its environment.

When quantizing a classical Hamiltonian there is some freedom when choosing the operator order, and these choices lead to differences in the ground state energy.

When there is interaction among the subsystems, the total Hamiltonian contains terms that do not commute with the angular operators acting on the subsystems only.

When the logarithm of the transfer operator corresponds to a quantum Hamiltonian, the eigenvalues will typically be very closely spaced, and thus even a very narrow and carefully selected ensemble of quantum states will encompass a large number of very different fractal eigenstates with non-zero support over the entire volume.

When the Hamiltonian of a system ( or the Lagrangian ) has a certain symmetry, but the ground state ( i. e., the vacuum ) does not, then one says that spontaneous symmetry breaking ( SSB ) has taken place.

When the Hamiltonian has the form of eq.

When restricted to a non-relativistic Coulomb Hamiltonian, conical intersections can be classified as symmetry-required, accidental symmetry-allowed, or accidental same-symmetry, according to the symmetry of the intersecting states.

When a finite dimensional Hamiltonian system is completely integrable in the Liouville sense,

* When, the Kneser graph always contains a Hamiltonian cycle.

When Heidegger and Sartre speak of a contrast between being and existence, they may be right, I don't know, but their language is too philosophical for me.

When they express themselves it is incandescent hatred that shines forth, the rage of repudiation, the ecstasy of negation.

When I try to work out my reasons for feeling that this passage is of critical significance, I come up with the following ideas, which I shall express very briefly here and revert to in a later essay.

When the proprietor dies, the establishment should become a corporation until it is either acquired by another proprietor or the government decides to drop it.

When the reactionary response is thus bolstered by an intellectual defense, the characteristics of that defense are explicable only in terms of the basic attitudes of unanalyzed reaction.

When I take over Taliesin, the first thing I'll do is fire you ''.

When someone in the audience rose and asked how does it feel to be a celebrity, Carl said, `` A celebrity is a fellow who eats celery with celerity ''.

When decision makers act within this frame they determine whether a claim put forward in the name of religion is to be accepted by the larger community as appropriate to religion.

When we consider the disorganized state of the world community, and the legacy of predispositions adversely directed against all who are identified as Jews, it is obvious that the struggle for the minds and muscles of men needs to be prosecuted with increasing vigor and skill.

When we turn to Aristotle's ideas on the moral measure of literature, it is at once apparent that he is at times equally concerned about the influence of the art.

When their faith in civil liberties is tested against strong pressures of social expediency in specific issues, e.g., suppression of `` dangerous ideas '', many waver and give in.

There is, of course, nothing new about dystopias, for they belong to a literary tradition which, including also the closely related satiric utopias, stretches from at least as far back as the eighteenth century and Swift's Gulliver's Travels to the twentieth century and Zamiatin's We, Capek's War With The Newts, Huxley's Brave New World, E. M. Forster's `` The Machine Stops '', C. S. Lewis's That Hideous Strength, and Orwell's Nineteen Eighty-Four, and which in science fiction is represented before the present deluge as early as Wells's trilogy, The Time Machine, `` A Story Of The Days To Come '', and When The Sleeper Wakes, and as recently as Jack Williamson's `` With Folded Hands '' ( 1947 ), the classic story of men replaced by their own robots.

When I first came across Samuel Johnson's pronouncement, `` the remedy for the ills of life is palliative rather than radical '', it seemed to me to sum up the profoundest of political and social truths.

When all else fails, it is argued that open sessions slow down governmental operations.

When a person has thoughtlessly or deliberately caused us pain or hardship it is not always easy to say, `` Just forget it ''.

When a person meets God's requirements for the experience of forgiveness he is forgiven.

When I hold my son he stiffens his whole body in my arms until he is as straight and stiff as a board.

When different colors are used, she is just as likely to color trees purple, hair green, etc..

When we become firm enough to stand for those ideals which we know to be right, when we become hard enough to refuse to aid nations which do not permit self-determination, when we become strong enough to resist any more drifts towards socialism in our own Nation, when we recognize that our enemy is Communism not war, and when we realize that concessions to Communists do not insure peace or freedom, then, and only then will we no longer be `` soft ''.

When one powerful nation strives to emulate the success of another, it is only natural.

When a man is laid to rest, he is entitled to stay put.

When I talked to Ching about it, he said, Everyone can learn, if he is not a Reactionary or lazy.

When having legal status recognized, or defined in law, as in ancient China, concubinage was akin, although inferior, to marriage.

When dealing with graded algebras, the commutator is usually replaced by the graded commutator, defined in homogeneous components as

When an order has been defined in this way, a sorting algorithm can be used to put a list of any number of items into that order.

When the plasma goes upward from the footpoints towards the loop top, as it always occurs during the initial phase of a compact flare, it is defined as chromospheric evaporation.

When defined for a topological vector space there is a subspace of this dual space, corresponding to continuous linear functionals, which constitutes a continuous dual space.

When the database is ready ( all its data structures and other needed components are defined ) it is typically populated with initial application's data ( database initialization, which is typically a distinct project ; in many cases using specialized DBMS interfaces that support bulk insertion ) before making it operational.

When the determinant is equal to one, the linear mapping defined by the matrix is equi-areal and orientation-preserving.

When setting up PBXs to run a DPNSS connection one end must be defined as the primary or ' A ' end.

When used in science, for example geology, eras denote clearly defined periods of time of arbitrary but well defined length, such as for example the Mesozoic Era from 252 Ma – 66 Ma, delimited by a start event and an end event.

When England switched to the shorter foot in the late 13th century, rods and furlongs remained unchanged, since property boundaries were already defined in rods and furlongs.

When an object changes its color smoothly, the animation can be defined by keyframes — the first showing its original color, and the second showing its final color.

When Edward Witten named M-theory, he did not specify what the M stood for — perhaps because the nascent theory was not fully defined.

When there has also been an osteoporotic fracture ( also termed " low trauma-fracture " or " fragility fracture "), defined as one that occurs as a result of a fall from a standing height, the term " severe or established " osteoporosis is used.

When the exact chromaticities of the red, green, and blue primaries are defined, the color model then becomes an absolute color space, such as sRGB or Adobe RGB ; see RGB color spaces for more details.

When a tabloid is defined as " roughly " and commonly " half the size of a broadsheet ," confusion can arise because " Many broadsheets measure roughly ", half of which is roughly not.

When it becomes necessary to distinguish these special vectors from vectors as defined in pure mathematics, they are sometimes referred to as geometric, spatial, or Euclidean vectors.

When the length of vectors is defined, it is possible to also define a dot product — a scalar-valued product of two vectors — which gives a convenient algebraic characterization of both length ( the square root of the dot product of a vector by itself ) and angle ( a function of the dot product between any two vectors ).

When using this convention, in contrast to the other convention, the defined handedness of the wave matches the handedness of the screw type nature of the field in space.

When practiced outside the laws of war, it is often defined as terrorism, though rarely by its practitioners or their supporters.

When reactive elements such as capacitors, inductors, or transmission lines are involved in a circuit to which AC or time-varying voltage or current is applied, the relationship between voltage and current becomes the solution to a differential equation, so Ohm's law ( as defined above ) does not directly apply since that form contains only resistances having value R, not complex impedances which may contain capacitance (" C ") or inductance (" L ").

When abstraction proceeds into the operations defined, enabling objects of different types to be substituted, it is called polymorphism.

:( a ) When people and organizations focus primarily on quality, defined by the following ratio,

When used in computer graphics to render scenes composed of planar polygons, the partitioning planes are frequently ( but not always ) chosen to coincide with the planes defined by polygons in the scene.

When both descendants are similar in a particular respect, evolution is defined as parallel if the ancestors considered were also similar, and convergent if they were not.