right-hand side of the equation con-
sists of the product of the same
eigenfunction and a constant. Eigen-
value equations occur in quantum
mechanics, with the eigenvalues
being the values of the quantized
quantities. In particular, the
Schrödinger equation is an eigen-
value equation with the allowed
quantized energy levels being the
eigenvalues of this equation.Einstein, Albert(1879–1955) Ger-
man-born US physicist, who took
Swiss nationality in 1901. A year
later he went to work in the Bern
patent ofÜce. In 1905 he published
Üve enormously inÛuential papers,
one on *Brownian movement, one
on the *photoelectric effect, one on
the special theory of relativity, and
one on energy and inertia (which in-
cluded the famous expression E =
mc^2 ). In 1915 he published the gen-
eral theory of relativity, concerned
mainly with gravitation. In 1921 he
was awarded the Nobel Prize for
physics. In 1933, as a Jew, Einstein
decided to remain in the USA (where
he was lecturing), as Hitler had come
to power. For the remainder of his
life he sought a uniÜedÜeld theory.
In 1939 he informed President Roo-
sevelt that an atom bomb was feasi-
ble and that Germany might be able
to make one.
Einstein coefÜcientsCoefÜcients
used in the quantum theory of radia-
tion, related to the probability of a
transition occurring between the
ground state and an excited state (or
vice versa) in the processes of *in-
duced emission and *spontaneous
emission. For an atom exposed to
electromagnetic radiation, the rate of
absorption Rais given by Ra= Bρ,
where ρis the density of electromag-
netic radiation and B is the Einstein B
coefÜcientassociated with absorp-
tion. The rate of induced emission isalso given by Bρ, with the coefÜcient
B of induced emission being equal to
the coefÜcient of absorption. The rate
of spontaneous emission is given by
A, where A is the Einstein A coefÜ-
cient of spontaneous emission. The A
and B coefÜcients are related by A =
8 πhν^3 B/c^3 , where h is the Planck con-
stant, νis the frequency of electro-
magnetic radiation, and c is the speed
of light. The coefÜcients were put for-
ward by Albert *Einstein in 1916–17
in his analysis of the quantum theory
of radiation.Einstein equation1.The mass–
energy relationship announced by Al-
bert *Einstein in 1905 in the form E
= mc^2 , where E is a quantity of en-
ergy, m its mass, and c is the speed of
light. It presents the concept that en-
ergy possesses mass. 2.The relation-
ship Emax= hf–W, where Emaxis the
maximum kinetic energy of elec-
trons emitted in the photoemissive
effect, h is the Planck constant, f the
frequency of the incident radiation,
and W the *work function of the
emitter. This is also written Emax= hf- φe, where e is the electronic charge
and φa potential difference, also
called the work function. (Sometimes
W and φare distinguished as work
function energy and work function
potential.) The equation can also be
applied to photoemission from gases,
when it has the form: E = hf– I,
where I is the ionization potential of
the gas.
einsteiniumSymbol Es. A radio-
active metallic transuranic element
belonging to the *actinoids; a.n. 99;
mass number of the most stable iso-
tope 254 (half-life 270 days). Eleven
isotopes are known. The element was
Ürst identiÜed by A. Ghiorso and as-
sociates in debris from theÜrst hy-
drogen bomb explosion in 1952.
Microgram quantities of the elementEinstein, Albert 192e