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…I think it is safe to say that
no one understands Quantum
Mechanics…
Richard
Feynman
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View Full Document Postulate 1: The state of a quantum mechanical
system is
completely speciFed by a function
Ψ
(
r
,t)
that depends on the coordinates of the particle(s)
and on time. This function, called the
wave function
or state function, has the important property that
Ψ
±
(
r
,t)
Ψ
(
r
,t) is the probability that the particle lies in the
volume element
d
τ
located at
r
at time t .
The
wavefunction is normalized and “well
behaved”
(single valued, continuous with continuous
derivative)
Acceptable as wavefunctions?
•
exp (x)
between 0 and infinity
•
exp (x) between –infinity and +infinity
•
1/sin(x) in (1,1)
•
exp (x) between –infinity and +infinity
Postulate 2:
To every observable in classical
mechanics there corresponds a
linear,
Hermitian operator
in quantum mechanics.
Real eigenvalues and
orthogonal eigenfunctions
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View Full Document Angular
momentum
Total energy
Multiply by
Potential energy
Kinetic energy
Momentum
Multiply by
Position
Operation
Symbol
Symbol
Name
Operator
Operator
Observable
Observable
Angular momentum
Classical definition:
Quantum Mechanical
definition:
Cross product
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mechanical operators are orthogonal
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This note was uploaded on 02/06/2011 for the course CHE 110A taught by Professor Mccurdy during the Fall '09 term at UC Davis.
 Fall '09
 Mccurdy

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