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In classical mechanics ``observables'' (the technical term for anything
that can be measured) are represented by numbers. Think e.g., of
x, y, z, px, py, pz, E, .... In quantum mechanics
``observables'' are often quantised, they cannot take on all possible
values: how to represent such quantities?
We have already seen that energy and momentum are represented by operators,
and
= -
+ V(x) |
(8.2) |
Let me look at the Hamiltonian, the energy operator. We know that its
normalisable solutions (eigenvalues) are discrete.
The numbers En are called the eigenvalues, and the functions
(x)
the eigenfunctions of the operator
. Our postulate says that
the only possible outcomes of any experiment where we measure energy
are the values En!