### Re: Is kinetic energy quanta (quantified) like electron clouds?

Date: Thu May 17 09:54:47 2007
Posted By: Joe Fitzsimons, Grad student, Quantum and Nanotechnology Theory Group, Department of Materials, Oxford University
Area of science: Physics
ID: 1179338668.Ph
Message:
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Hi Robert,

You ask some excellent questions, and I will do my best to answer them for
you.

The way a quantum system behaves is governed by what is called the
Hamiltonian of the system. The Hamiltonian is the sum of the kinetic and
potential energy operators, and so it's values correspond to the total
energy of the system. In quantum mechanics the Hamiltonian can only give
discrete values, and so the possible values of the total energy are quantized.

The important thing to note is that this says nothing about the values of
the kinetic or potential energies.

Quantum mechanics is a little strange. It allows for particles to be in
more than one state at a time (i.e. two or more places at the same time, or
two or more energies). When you measure the particle, you will only ever
see it in one of these states, but it is possible to show that it was in a
superposition by indirect means (see the link concerning the double slit
experiment below).

Any thing we can observe (or measure) has what is called an operator
associated with it. The operator is a mathematical device which describes
what will happen to the particle when you measure it. If you can define the
correct type of operator for something, then you can measure it.

The Hamiltonian is the operator which correspond to measuring the total
energy of a system. It is also possible to define a kinetic energy
operator. The interesting thing here, however, is that what might be one of
the allowed kinetic energy levels may correspond to a superposition of
total energy levels, and vica versa.

For experiments we are almost always only interested in the total energy
level, as given by the Hamiltonian. One reason for this is because it
defines the shells occupied by electrons (these are the clouds you
mentioned in the title).

I hope this goes someway towards answering the first part of your question.
I'm afraid that to show this is true requires quite a bit of mathematics. I
have included a link on Hamiltonians and on Operators in quantum mechanics
below too, in case you do require further information.

to an atom. The answer to this largely depends on how you add energy.

If you add energy to both the nucleus and the electrons, then it is
possible to simply accelerate the entire atom, with little or no effect on
the electrons. This is what happens when you throw a baseball for example.

If however the atom absorbs the energy internally, like when two atoms
collide, or when an atom absorbs a photon (a particle of light), then the
electrons are excited to higher energy levels. If you add
enough energy, then it is possible for an electron to break free, with the
atom becoming an ion. The energy required to achieve this is known as the
ionisation energy.

Electrons which are in excited states like this often decay into lower
energy states by emitting a photon, through spontaneous emission. The
probability of this happening within a given time period usually depend on
how big a difference there is in energy levels between the initial energy
level and the final energy level, although the can be added complications
as not all transitions are possible (the laws governing these are known as
selection rules).

Any atom that can decay to a lower state through photon emission will, but
the time taken for this to happen may be very long. Nuclear spins, for
example, take a very long time to decay.

While the exact time taken for a photon to be emitted is probabilistic (due
to its quantum mechanical nature) there is a characteristic time associated
with it known as the lifetime of the state. This is very similar to the

Joe

Operators in
Physics

Hamiltonians
in Quantum Mechanics

Hamiltonians
in Quantum Mechanics

Spontaneous
Photon Emission

Ionisation Energy

```

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