and show properties such as interference,
diffraction
Slide 20
The Davisson Germer Experiment
Proving the wave properties of electrons (matter!)
Intensity variation in diffracted beam shows constructive and destructive interference of wave
Slide 21
Principles of Quantum Mechanics The Wavefunction
Y(position, time)
In quantum mechanics, an electron, just like any other particle, is described by a
Contains all information there is to
know about the particle
Important
Slide 22
is the wavefunction,
V(r) the potential energy and
E the total energy
More on than in Hilary Term
Slide 23
Instead of Cartesian (x,y,z) the maths works out easier if we use a different coordinate system:
y
x
z
x = r sin cos
y = r sin sin
z = r cos
(takes advantage of
the spherical symmetry
of the system)
Slide 24
So Schrödinger’s Equation becomes .
More on than in Hilary Term
Slide 25
We separate the wavefunction into 2 parts:
a radial part R(r) and
an angular part Y(,),
such that =
The solution introduces 3 quantum numbers:
Important
which can be solved exactly for the H-atom with the solutions called orbitals, more specifically, atomic orbitals.
Slide 26
which can be solved exactly for the H-atom with the solutions called orbitals, more specifically, atomic orbitals.
We separate the wavefunction into 2 parts:
a radial part R(r) and
an angular part Y(,),
such that =R(r)Y(,)
The solution introduces 3 quantum numbers:
Important
Slide 27
quantum numbers arise in the solution;
R(r) gives rise to:
the principal quantum number, n
Y(,) yields:
the orbital angular momentum quantum number, l and the magnetic quantum number, ml
i.e., =Rn,l(r)Yl,m(,)
Important
Slide 28
The values of n, l, & ml