With de Broglie's suggestion of the existence of electron matter waves in 1924, and for a short time before the full 1926 Schrödinger equation treatment of hydrogen like atom, a Bohr electron " wavelength " could be seen to be a function of its momentum, and thus a Bohr orbiting electron was seen to orbit in a circle at a multiple of its half-wavelength ( this historically incorrect Bohr model is still occasionally taught to students ).

* Conservation of Momentum: This equation applies Newton's second law of motion to a continuum, whereby force is equal to the time derivative of momentum.

He showed that if ρ ( x, t ) is the density of Brownian particles at point x at time t, then ρ satisfies the diffusion equation:

Assuming that all the particles start from the origin at the initial time t = 0, the diffusion equation has the solution

Once the electronic and nuclear variables are separated ( within the Born – Oppenheimer representation ), in the time-dependent approach, the wave packet corresponding to the nuclear degrees of freedom is propagated via the time evolution operator ( physics ) associated to the time-dependent Schrödinger equation ( for the full molecular Hamiltonian ).

Some cosmologists and physicists argue that a challenge to the cosmological argument is the nature of time: " One finds that time just disappears from the Wheeler – DeWitt equation " ( Carlo Rovelli ).

By direct substitution, the solution to this equation can be readily shown to be the scalar Green's function, which in the spherical coordinate system ( and using the physics time convention ) is:

If the amount to be paid at time 0 ( now ) for all the future cash flows is known, then that amount can be substituted for DPV and the equation can be solved for i, that is the internal rate of return.

( The relation is either a differential equation, difference equation or other time scale.

The equation gives the time derivative, represented by the dot, of a trajectory x ( t ) on the phase space starting at some point x < sub > 0 </ sub >.

There is no need for higher order derivatives in the equation, nor for time dependence in v ( x ) because these can be eliminated by considering systems of higher dimensions.

“ The symbolism that Diophantus introduced for the first time, and undoubtedly devised himself, provided a short and readily comprehensible means of expressing an equation ...

The variation of orbital speed accounts for part of the equation of time.

Introduced in 1949 the Redlich – Kwong equation of state was a considerable improvement over other equations of the time.

In 1923, while writing the appendix for the Italian edition of the book The Mathematical Theory of Relativity by A. Kopff, Enrico Fermi pointed out, for the first time, that hidden inside the famous Einstein equation (), there was an enormous amount of nuclear potential energy to be exploited.

The date and approximate time of a specific full moon ( assuming a circular orbit ) can be calculated from the following equation:

The speculative equation factors in: the rate of star formation in the galaxy ; the fraction of stars with planets and the number per star that are habitable ; the fraction of those planets which develop life, the fraction of intelligent life, and the further fraction of detectable technological intelligent life ; and finally the length of time such civilizations are detectable.

An important example is the case where is at a steady state, i. e. the concentration does not change by time, so that the left part of the above equation is identically zero.

This event may be up to 16 minutes away from noon GMT ( a discrepancy calculated by the equation of time ).

The details are more complex than described here: see the articles on Universal Time and on the equation of time for more details.

Rather than the amount of charge and its velocity in electric and magnetic fields, this equation relates the energy flux ( flow of energy per unit time per unit distance ) in the fields to the force exerted on a charge distribution.

The centrifugal force term in this equation is called a " fictitious force ", " apparent force ", or " pseudo force ", as its value varies with the rate of rotation of the frame of reference.

The most common way to formalize this is by defining a field as a set together with two operations, usually called addition and multiplication, and denoted by + and ·, respectively, such that the following axioms hold ; subtraction and division are defined implicitly in terms of the inverse operations of addition and multiplication :< ref group =" note "> That is, the axiom for addition only assumes a binary operation The axiom of inverse allows one to define a unary operation that sends an element to its negative ( its additive inverse ); this is not taken as given, but is implicitly defined in terms of addition as " is the unique b such that ", " implicitly " because it is defined in terms of solving an equation — and one then defines the binary operation of subtraction, also denoted by "−", as in terms of addition and additive inverse.

A related concept, the " Finagle factor ", is an ad hoc multiplicative or additive term in an equation which can only be justified by the fact that it gives more correct results.

", introducing the equation E = mc².

When v is larger than c, the denominator in the equation for the energy is " imaginary ", as the value inside the square root is negative.

His dissertation, entitled, " Solutions of the Mathieu equation of period 4 pi and certain related functions ", was beyond the comprehension of the chemistry and physics faculty, and only when some members of the mathematics department, including the chairman, insisted that the work was good enough that they would grant the doctorate if the chemistry department would not, was he granted a Ph. D. in chemistry in 1935.

For example, Sir Arthur Stanley Eddington claimed that the cosmological constant version of the vacuum field equation expressed the " epistemological " property that the universe is " self-gauging ", and Erwin Schrödinger's pure-affine theory using a simple variational principle produced the field equation with a cosmological term.

The kepstrum, which stands for " Kolmogorov equation power series time response ", is similar to the cepstrum and has the same relation to it as statistical average has to expected value, i. e. cepstrum is the empirically measured quantity while kepstrum is the theoretical quantity.

Because " a double negative is an affirmative ", this becomes a functional equation

* John C. Shedd and Mayo D. Hershey ," The History of Ohm's Law ", Popular Science, December 1913, pages 599-614, Bonnier Corporation ISSN 0161-7370, gives the history of Ohm's investigations, prior work, Ohm's false equation in the first paper, illustration of Ohm's experimental apparatus.

The time-dependent Schrödinger equation predicts that wavefunctions can form standing waves, called stationary states ( also called " orbitals ", as in atomic orbitals or molecular orbitals ).

In Phoenician, as well as Hebrew, the Semitic root qdm signifies " the east ", the Levantine origin of " Kdm " himself, according to the Greek mythographers ; the equation of Kadmos with the Semitic qdm was traced to a publication of 1646 by R. B. Edwards.

Because she is Artemis Daphnaia, the god's sister ," observed the Freudian anthropologist Géza Róheim, and Joseph Fontenrose concurs ; boldly stating such a one-to-one identity doubtless oversimplifies the picture: " the equation of Artemis and Daphne in the transformation myth itself clearly cannot work ", observes Lightfoot.

If every ion is a " spectator ion ", then there was no reaction, and the net ionic equation is null.

Despite this usage of " covariant ", it is more accurate to say that the Klein – Gordon and Dirac equations are invariant, and that the Schrödinger equation is not invariant.

Considerable confusion exists in the literature of this area because: ( 1 ) many sources do not distinguish between A < sub > G </ sub > and A < sub > 0 </ sub >, but just use the symbol A ( and sometimes the name " Richardson constant ") indiscriminately ; ( 2 ) equations with and without the correction factor here denoted by λ < sub > R </ sub > are both given the same name ; and ( 3 ) a variety of names exist for these equations, including " Richardson equation ", " Dushman's equation ", " Richardson – Dushman equation " and " Richard – Laue – Dushman equation ".

The equation is used for the mathematical process of solving the problem.

Using the same figures as for the previous example, the equation becomes: Af

The total volume of the system above the reference height is Af, and H can be eliminated to obtain an equation for the total potential energy of the system in terms of H.

Thomas also presents a simple equation for deriving an index of persistence, which weights not only the number of stems ( ' roots ' ) per meaning, but their relative frequency.

Atomic orbitals can be the hydrogen-like " orbitals " which are exact solutions to the Schrödinger equation for a hydrogen-like " atom " ( i. e., an atom with one electron ).

In the Schrödinger equation for this system of one negative and one positive particle, the atomic orbitals are the eigenstates of the Hamiltonian operator for the energy.

We make several assumptions to derive the momentum balance equation for an acoustic medium.

The equation for the conservation of mass in a fluid volume ( without any mass sources or sinks ) is given by

The equation for the conservation of mass for an acoustic medium can also be derived in a manner similar to that used for the conservation of momentum.

In order to close the system of equations we need an equation of state for the pressure.

The equation for the conservation of mass can similarly be written in cylindrical coordinates as

Dirac realised that his relativistic version of the Schrödinger wave equation for electrons predicted the possibility of antielectrons.

Such temperature changes can be quantified using the ideal gas law, or the hydrostatic equation for atmospheric processes.

The mathematical equation for an ideal gas undergoing a reversible ( i. e., no entropy generation ) adiabatic process is

If it is assumed that all color values are premultiplied by their alpha values (), we can rewrite the equation for output color as:

In analytic geometry, any equation involving the coordinates specifies a subset of the plane, namely the solution set for the equation.

These points form a line, and y = x is said to be the equation for this line.

The equation x < sup > 2 </ sup > + y < sup > 2 </ sup > = r < sup > 2 </ sup > is the equation for any circle with a radius of r.

This equation is incorrect for the calculation of drag in most cases.