Physics for Electronics Engineering: Unit II: Electrical and Magnetic Properties of Materials
Degenerate States and Tunneling
Electrical Properties of Materials
The same energy eigen value but different eigen functions. Such a state of energy levels is called degenerate state.
DEGENERATE STATES
It
is seen from equations (3) and (4) that for several combinations of quantum
numbers, we have the same energy eigen value but different eigen functions.
Such a state of energy levels is called degenerate state.
The three combinations of quantum numbers, (112), (121) and (211), which give the same eigen value but different eigen functions are called 3-fold degenerate state.
Non-degenerate state:
When
only one wave function corresponds to the energy eigen value, such a state is
called non-degenerate state.
Suppose
nx = 2, ny = 2, nz = 2
TUNNELING
i.
According to classical ideas, a particle striking a hard wall has no chance of
leaking through it. But, the behaviour of a quantum particle is different due
to the wave nature associated with it.
ii.
We know that when an electromagnetic wave strikes at the interface of two
media, it is partly reflected and partly transmitted through the interface and
enters the second medium.
iii.
In a similar way the de Broglie wave also has a possibility of getting partly
reflected from the boundary of the potential well and partly penetrating
through the barrier.
iv.
Fig. 2.9 shows a particle with energy E< V approaching potential barrier of
height V.
v. An electron of total energy E approaches the barrier from the left. From the view-point of classical physics, the electron would be reflected from the barrier because its energy E is less than V.
vi.
For the particle to overcome the potential barrier, it must have an energy
equal to or greater than V.
Quantum
mechanics leads to an entirely new result. It shows that there is a finite
chance for the electron to leak to the other side of the barrier.
It
is noted that the electron tunneled through the potential barrier and hence in
quantum mechanics, this phenomenon is called tunneling.
The
transmission of electrons through the barrier is known as barrier penetration.
Physics for Electronics Engineering: Unit II: Electrical and Magnetic Properties of Materials : Tag: : Electrical Properties of Materials - Degenerate States and Tunneling
Physics for Electronics Engineering: Unit II: Electrical and Magnetic Properties of Materials
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Physics for Electronics Engineering
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