professor Dave again let's take a look
at the Schrodinger equation through the
work of Planck and Einstein we were
forced to accept that energy is
quantized and that light exhibits wave
particle duality then debroglie I
extended this duality to include matter
as well meaning that all matter has a
wavelength from a tiny electron to your
whole body to a massive star however an
object's wavelength is inversely
proportional to its mass so objects
bigger than a molecule have a wavelength
that is so tiny that it is completely
negligible but an electron is incredibly
small so small that its wavelength is
indeed relevant being around the size of
an atom so we must view electrons as
both particles and waves from now on
therefore we must discuss the wave
nature of the electron so what kind of
wave might this be we can regard an
electron in an atom as a standing wave
just like the kind we learned about in
classical physics except that rather
than something like a plucked guitar
string an electron is a circular
standing wave surrounding the nucleus if
we understand this it becomes
immediately apparent why quantization of
energy applies to the electron because
any circular standing wave must have an
integer number of wavelengths in order
to exist given that an increasing number
of wavelengths means more energy carried
by the wave we can see the Bohr model
for the hydrogen atom begin to emerge as
we imagine a standing wave with one
wavelength and then two and then three
and so forth this is the reason that an
electron in an atom can only inhabit a
discrete set of energy levels the
circular standing wave that represents
the electron can only have an integer
number of wavelengths when an electron
is struck by a photon of a particular
this energy is absorbed promoting the
electron to a higher energy state and
increasing the number of wavelengths
contained within the standing wave this
is why the electron goes to inhabit a
higher energy level and this is what is
fundamentally occurring during electron
excitation furthermore it is the
constructive interference of these
standing waves that explains how orbital
overlap results in covalent bonding so
we can enjoy a little more clarity in
our understanding of chemistry thanks to
modern physics once it was realized that
electrons exhibit wave behavior the
physics community set out to find a
mathematical model that could describe
this behavior
Erwin Schrodinger achieved this goal in
1925 when he developed his Schrodinger
equation which incorporated the
debroglie a relation this is a
differential equation which utilizes
concepts in mathematics that are beyond
the scope of this series but we can
certainly discuss the conceptual
implications of the equation essentially
just as F equals MA applies to Newtonian
systems the Schrodinger equation applies
to quantum systems by describing the
system's three-dimensional wave function
represented by the Greek letter sy in
this equation this term is called the
Hamiltonian operator which is a set of
mathematical operations that describes
all the interactions that are affecting
the state of the system which can be
interpreted as the total energy of a
particle but while the Schrodinger
equation can calculate the wave function
of a system it does not specifically
reveal what the wave function is Max
Born proposed that we interpret the wave
function as a probability amplitude
where the square of the magnitude of the
wave function describes the probability
of an electron existing in a particular
location looking back at the double slit
experiment we understand the diffraction
pattern as illustrating this wave of
probability
the pattern is not the electron itself
it is the probability that an electron
will arrive at each location on the
screen we can't predict where one
electron will go only the probability
that it will arrive at a particular
location if many electrons arrive at the
screen it becomes apparent how their
distribution obeys the wave function so
the Schrodinger equation does compute
the wave function deterministically but
what the wave function tells us is
probabilistic in nature this idea that
nature is probabilistic on the most
fundamental level was a lot for the
scientific community to handle at the
time and still is for some so just the
way sound waves are mechanical waves and
light waves are oscillations in an
electromagnetic field an electron can be
considered a cloud of probability
density there are many such
interpretations of quantum mechanics
which involve different ways of viewing
the relationship between the wave
function experimental results and the
nature of reality and there is still no
firm consensus as to which view is
correct be it the Copenhagen
interpretation many-worlds
interpretation or a number of others but
before you choose a camp let's keep
moving through the development of
quantum mechanics which means we will
need to consult Verner Heisenberg thanks
for watching guys subscribe to my
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professor Dave explains at gmail.com
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