right-hand side of the equation consists of the product of the same
eigenfunction and a constant. Eigenvalue equations occur in quantum
mechanics, with the eigenvalues
being the values of the quantized
quantities. In particular, the
Schrödinger equation is an eigenvalue equation with the allowed
quantized energy levels being the
eigenvalues of this equation.
Einstein, Albert (1879–1955) German-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 included the famous expression E =
mc
2 ). In 1915 he published the general 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 uniÜed Üeld theory.
In 1939 he informed President Roosevelt that an atom bomb was feasible and that Germany might be able
to make one.
Einstein coefÜcients CoefÜcients
used in the quantum theory of radiation, related to the probability of a
transition occurring between the
ground state and an excited state (or
vice versa) in the processes of *induced emission and *spontaneous
emission. For an atom exposed to
electromagnetic radiation, the rate of
absorption R a is given by R a = Bρ,
where ρ is the density of electromagnetic radiation and B is the Einstein B
coefÜcient associated with absorption. The rate of induced emission is
also 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 coefÜcient of spontaneous emission. The A
and B coefÜcients are related by A =
8πhν
3
B/c
3 , where h is the Planck constant, ν is the frequency of electromagnetic radiation, and c is the speed
of light. The coefÜcients were put forward by Albert *Einstein in 1916–17
in his analysis of the quantum theory
of radiation.
Einstein equation 1. The mass–
energy relationship announced by Albert *Einstein in 1905 in the form E
= mc
2
, where E is a quantity of energy, m its mass, and c is the speed of
light. It presents the concept that energy possesses mass. 2. The relationship E max = hf – W, where E max is the
maximum kinetic energy of electrons 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 E max = hf
– φe, where e is the electronic charge
and φ a potential difference, also
called the work function. (Sometimes
W and φ are 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.
einsteinium Symbol Es. A radioactive metallic transuranic element
belonging to the *actinoids; a.n. 99;
mass number of the most stable isotope 254 (half-life 270 days). Eleven
isotopes are known. The element was
Ürst identiÜed by A. Ghiorso and associates in debris from the Ürst hydrogen bomb explosion in 1952.
Microgram quantities of the element
Einstein, Albert
192
e
www.AzShimi.ir www.AzShimi.com
eigenfunction and a constant. Eigenvalue equations occur in quantum
mechanics, with the eigenvalues
being the values of the quantized
quantities. In particular, the
Schrödinger equation is an eigenvalue equation with the allowed
quantized energy levels being the
eigenvalues of this equation.
Einstein, Albert (1879–1955) German-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 included the famous expression E =
mc
2 ). In 1915 he published the general 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 uniÜed Üeld theory.
In 1939 he informed President Roosevelt that an atom bomb was feasible and that Germany might be able
to make one.
Einstein coefÜcients CoefÜcients
used in the quantum theory of radiation, related to the probability of a
transition occurring between the
ground state and an excited state (or
vice versa) in the processes of *induced emission and *spontaneous
emission. For an atom exposed to
electromagnetic radiation, the rate of
absorption R a is given by R a = Bρ,
where ρ is the density of electromagnetic radiation and B is the Einstein B
coefÜcient associated with absorption. The rate of induced emission is
also 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 coefÜcient of spontaneous emission. The A
and B coefÜcients are related by A =
8πhν
3
B/c
3 , where h is the Planck constant, ν is the frequency of electromagnetic radiation, and c is the speed
of light. The coefÜcients were put forward by Albert *Einstein in 1916–17
in his analysis of the quantum theory
of radiation.
Einstein equation 1. The mass–
energy relationship announced by Albert *Einstein in 1905 in the form E
= mc
2
, where E is a quantity of energy, m its mass, and c is the speed of
light. It presents the concept that energy possesses mass. 2. The relationship E max = hf – W, where E max is the
maximum kinetic energy of electrons 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 E max = hf
– φe, where e is the electronic charge
and φ a potential difference, also
called the work function. (Sometimes
W and φ are 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.
einsteinium Symbol Es. A radioactive metallic transuranic element
belonging to the *actinoids; a.n. 99;
mass number of the most stable isotope 254 (half-life 270 days). Eleven
isotopes are known. The element was
Ürst identiÜed by A. Ghiorso and associates in debris from the Ürst hydrogen bomb explosion in 1952.
Microgram quantities of the element
Einstein, Albert
192
e
www.AzShimi.ir www.AzShimi.com