Heyy guys whats up hello well the topic today
is wave function and why is wave function
a complex valued function now the wave function
in the most general sense is the function
that describes the wave or we can say that
it is the collection of all the possible states
where one is supposed to find an electron
now why do we have to collect these points
rather than just use the classical mechanics
this is because of the some of the assumptions
of the quantum mechanics now see in classical
mechanics the objects have pre-defined location
such as these i could just use the cartesian
coordinate to locate this okay it will be
of no big deal right but in case of quantum
mechanics this is not the case you have the
laws of motion for the classical object f=ma
which is the second degree differential equation
now if you solve this equation you get a pre-defined
location but if you solve the quantum mechanics
you don't have a predefined locations but
you just have these hazes of probability where
you can you know just you can just predict
okay maybe here maybe here you can just give
them a probability and you you construct a
space okay where one is most likely to found
an electron find an electron okay so why is
there a why why in quantum mechanics you cannot
actually have a predefined location this is
because of the assumptions of quantum mechanics
the first assumption says that the electrons
like particles are not actually particles
but when they are moving through space when
they are moving through space get this when
they are moving through space they have very
greater velocity which is of the order of
like 10^6 m/s say the hydrogen atom in the
sorry electron in the hydrogen atom first
orbital/orbit has velocity of c/137 which is not precisely
orbit,orbit is the classical concept we have
orbitals in quantum mechanics now what you
need to understand is that particles moving
with that velocity will never show the particle
nature but instead they will show the wave
nature they will be spread out in the in the
space and they can be simply represented by
the superimposition of large number of waves
where the maxima will give the place where
one is most likely to find an electron now
the another implications of the assumptions
of quantum mechanics is that the heisenberg's
uncertainty principle which is going to tell
you that the position and momentum of the
particle cannot be measured precisely at the
same time more accurately will you try to
find one quantity the less accurate the other
quantity becomes due to this reason this is
simply trying to tell you is that the zero
kelvin is not attainable if you actually get
to zero kelvin the quantum mechanics will
sink the quantum mechanics will seize to work
okay we need a new mechanics quantum mechanics
is not going to work at that point so if you
have so if you have an electron it is an intrinsic
property of an electron to have that uncertainty
if someone is going to ask you about the spin
of an electron you just say that this is an
intrinsic property right in the similar manner
it is not the default it is not the fault
of our instruments to not being able to measure
its to measure its properties but it is simply
something intrinsic okay you just cannot do
that this is the idea that Einstein always
hated how can some system that can be observed
cannot be measured precisely okay now what
you need to understand is that one of the
best way to understand the wave function is
to look at a fan okay now say that this fan
right now have four fins right say that it
only has one fin okay for the simplicity because
the pauli's exclusion principle principle
is going to apply to it and there is only
going to be two electrons right but here is
four so lets just say that this is an electron
and at rest it is a particle right so but
when i start moving it when it starts moving
like this how the so it is all the places
at the same time and when it stops when you
stop it you just get this you just like its
like using an operator like say if i use an
energy operator to a moving electron it just
does like this it is just going to tell you
the energy at this point it is not going to
tell you the energy at different points okay
it is just going to tell you the energy at
this point so you use an projection operator
whatever operator you wanna use you just get
a value at this point now you and yes now
this is where it gets interesting you can
perform the experiments thousand times and
thousand times you are gonna get different
results different values this is why you need
to plot all of these which is basically the
wave function or the concept of the orbitals
see how the electrons see they are at one
place at a time but whey they start moving
they are at all places at the same time this
is a very interesting concept now another
important thing to understand is that why
is wave function a complex valued function
now the complexity of a wave function can
be understood in this way first thing first
now if you have a water wave if you throw
a stone in a water you can actually see the
water wave you can actually see the sound
wave you know that there is a wave you know
that there is a disturbance in the pressure
of the air okay but you can never actually
see the waves generated by the electrons it
is not possible to visualize the wave nature
of electron you just have this ugh concept
that is fitting into the observations but
you cannot see the electrons or the wave nature
of electrons this is like talking about the
direct lattice and the reciprocal lattice
why we always deal with the reciprocal lattice
but not with the direct lattice this is because
you never have the direct lattice okay you
know in the real world okay you never have
the direct lattice you cannot actually see
these electrons or how they are or atoms how
they are arranged you just use the projection
or you just use x rays to sort of map this
into the new lattice and then you go to fourier
transform this lattice to get the direct lattice
in the similar way you cannot actually visualize
the wave nature of the electrons you just
have this intuition that yes electrons behave
like waves and this fits into the picture
this fits into the observation that we actually
calculate in our real life thats why we are
using this and thats what is important this
is why the wave function is complex valued
function because you cannot actually visualize
the wave nature of the particle and if you
think about it thats what quantum mechanics
is all about just trying to find if electron
is at this point at t=0 seconds where is it
most likely to be found at t=1seconds so you
sort of assign probabilities at different
points and then thats it if you find the position
of an electron you you have just condensed
an entire quantum system into the classical
system then you just do whatever the experiments
or the measurements you have to do with the
particles :) ;)
