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Quantum
mechanics introduced the concept of the duality of the particle and wave
descriptions of matter. A particle with a momentum, p, has an associated
wavelength, l,
and wavenumber, k, such that: p
= (h/2p)k
, where h is Planck's constant. Also, l
= 2p/k.
The
quantum state of the particle is described by a Wave function, y(r,
t), which depends on time, t, and position, r. The wave function is related
to the probability, dP(r, t), of the particle being in an element of volume,
d3r,
viz:
dP(r,
t) = C [ y(r,
t) ]2
d3r,
where C is a constant that ensures that the integral of the probability
over all space is unity.
In
many systems it is the time independent electron distribution that is of
interest. In this case the time independent wave function describes the
system. For the hydrogen atom, the lowest electronic state has a wavefunctionof
the form, y1S
= (Z3/pa3)0.5
exp( -Zr/a),
where a is the location of the maximum in the probability distribution. |
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