Curvature of Wave Functions
Schrdingers equation in the form
can be interpreted by saying that the left-hand side, the rate of change of slope, is
the curvature so the curvature of the function is pro
Roleoftemperature
Temperaturecausesquantumlocalizationtodecreaseastemperatureisincreased.
Thethermalwavelength
kisBoltzmannsconstant.
Considermethane:CH4
H
H
C
1.8
H
C
H
ThefourHsareidentical.Doweneed
Hellman-Feynman Theorem
Consider a system with a Hamiltonian
Let
be an eigenvector of
that depends on some parameters .
with eigenvalue
(16)
We further assume that
is normalized so that
(17)
The Hellm
calledtheHartreeequation.
Whenwetreattheelectronsasindistinguishable,wecannotusetheproductform.Rather,we
take
Again,weneedtocompute.
Wefind:
Notethesumsarenotrestricted.Thefirsttwobodyintegralgives
is
HAMILTONIAN AIMD
The next few lectures will treat the problem of quantum chemistry, a subfield of
quantum mechanics also known as molecular quantum mechanics. The idea of
quantum chemistry is to use o
Ground Motion Nuclear Evolution
In many cases, non-adiabatic effects can be neglected, and we may consider
motion only on the ground electronic surface described by:
(10)
Moreover, if nuclear quantum
electroniceigenvalueproblem:IntheBornOppenheimerapproximation,theelectronic
eigenvalueproblemtakestheform.
Let
wherexdenotestheelectroniccoordinates,andRdenotesthenuclearcoordinates.
Crudestapproximat
Born-Oppenheimer surfaces: full internuclear potential for each electronic surface is
given by
. On each Born-Oppenheimer surface, the nuclear
eigenvalue problem can be solved, which yields a set of l
The Born-Oppenheimer (named for its original inventors, Max Born and Robert
Oppenheimer) is based on the fact that nuclei are several thousand times heavier than
electrons. The proton, itself, is appr
MANUAL DEL CDIGO ELCTRICO COLOMBIANO (NTC 2050)
METODOS Y MATERIALES DE LAS INSTALACIONES
SECCIONES (300-324)
HUMBERTO CARLOS DAVILA POSADA
MAURICIO VILLA CASTAO
UNIVERSIDAD TECNOLOGICA DE PEREIRA
FAC