wave function
THE WAVE FUNCTION
The
experimental evidence for the wave properties of the electron and the success of
the Schrodinger equation in predicting the energy levels of the hydrogen atom indicate
that information about the physical properties of a particle moving under the influence
of a potential can be obtained from the wave
function. As we saw, this is a
continuous, single-valued function of the coordinates of the particle and the
time,and
its squared modulus must be integrable over all possible particle positions. It is
important to remember that, although the measurable properties of a system are derived
from the wave function, it is not itself a physical quantity.
However, it is a fundamental principle of quantum mechanics that the wave function contains all the information it is possible to obtain about a physical system in a particular state. The first postulate then concerns the existence of the wave function.
However, it is a fundamental principle of quantum mechanics that the wave function contains all the information it is possible to obtain about a physical system in a particular state. The first postulate then concerns the existence of the wave function.
Postulate
1- For every dynamical system there
exists a wave function that is a continuous,
square-integrable, single-valued function of the parameters of the system and
of time, and from which all possible prediction about the physical properties
of
the
system can be obtained.
This
statement covers the case of a particle moving in a potential where the“parameters
of the system” are the particle coordinates, but it also refers to more general
situations: for example, the parameters may be the coordinates of all the particles
of a many-body system and may include internal variables such as “spin.”
Notation
In
the previous chapters we used the symbol 
to
represent a general solution to the
to
represent a general solution to the
time-dependent
Schrodinger equation and the symbol u
(sometimes with a subscript)
as
the time-independent part of the wave function of a system in a state of given energy.
We shall continue this notation in the present chapter, and in addition we shall
use the symbol to represent a general wave function, whose time dependence we
are not explicitly considering, and the symbol
when quantity (not necessarily the energy) has a known value.the
system is in what we shall call an “eigenstate”—that is, when some dynamical
when quantity (not necessarily the energy) has a known value.the
system is in what we shall call an “eigenstate”—that is, when some dynamical
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