m

1
Postulates of Quantum Mechanics
(from quantum mechanics by Claude
Cohen-Tannoudji)
6th postulate The time evolution of the state
vector
is governed by the Schroedinger equation
where H(t) is the observable associated with the
total energy of the system.
1st postulate At a fixed time t0, the state of a
physical system is defined by specifying a ket
2
Postulates of Quantum Mechanics
(from quantum mechanics by Claude
Cohen-Tannoudji)
2nd postulate Every measurable physical quantity
is described by an operator
This operator is an observable.
3rd postulate The only possible result of the
measurement of a physical quantity
is one of the eigenvalues
of the corresponding observable
4th postulate (non-degenerate) When the physical
quantity
is measured on a system in the normalized state
the probability of
obtaining the eigenvalue
of the corresponding observable
is
where
is the normalized eigenvector of
associated with the eigenvalue
3
Physical interpretation of
is a probability density. The probability of
finding the particle in the volume element
at time
is
General solution for
Try separation of variables
Plug into TDSE to arrive at the pair of linked
equations
and
4
Orthogonality
For
which are different eigenvectors of
we have orthogonality
Let us prove this to introduce the bra/ket
notation used in the textbook