All right.
In over previous sessions.
We saw these two we equation's.
And we saw that how both these equations are one in the same.
Now, if you see over here, why is equal to it cause omega T minus kicks, this equation we saw is
the passcode to enter classical world.
The passcode to enter Quantum World is.
The segregation.
PSI equals to minus Omega T, minus K X..
So say.
Is basically the passcode to enter quantum world, anything you want to know about the quantum system?
The first thing you should know is say.
But what actually is the significance of CI?
CI actually is a complex number.
We know this particular equation.
That is scrutineers time dependent equation.
Now, if you see a complex number has an imaginary component and as such imaginary doesn't mean anything.
So if we try and solve this equation.
For say, we get.
This particular outcome.
Now, as I told you, there is no such any significance of, say.
But how can you make some sense?
Out of.
Site.
The significance can be achieved when we multiply.
PSI, which is a complex number with its complex conjugate.
Now we studied in complex numbers section that are complex conjugate is nothing, but we just inverse
the sign of an imaginary quantity.
That's it.
So over here, let's take an example, let's say is equal to A plus I.
B.
Then it's complex conjugate is.
I conjugate equals A minus I b now if you try and multiply both the complex number and its conjugate,
the output that you get is A squared plus B square.
Now, say, multiplied by its complex conjugate is even less PSI square.
Now, there is no physical significance of PSI Square because PSI Square is real, it's not complex,
there is no imaginary.
So there is a physical significance of size square.
So what is the significance of PSI Square?
PSI Square is called s the probability density.
So what exactly do you mean by a probability density?
Probability density means that within a finite range or a finite area, what is the proportional probability
to find without quantum particle in that region?
If the value of PSI Square is more, more is the probability of finding that quantum particle in that
region at that given time, for example, let's say the electron is continuously rotating.
Now, if I want to find out where exactly the pinpoint position of the electron is.
That is not possible in the quantum world, quantum world is probabilistic in nature.
Yep, because a quantum particle is associated with a group of vibs.
Yeah, so to find the position of an electron, we first need to derive PSI and then multiply PSI with
its complex conjugate and we get PSI squared, PSI squared will give you the probability of finding
the particle at a particular moment.
So for an atomic realism or subatomic level particles like this.
Always the quantum physics gets applied to it and you always deal with probability.
This is how.
Basically, PSI Square in one dimensional motion looks like, see if I integrate the region from A to
B, the probability of finding the electron is XY squared.
And basically.
This gives you the range that AK.
The electron would be from this region to this region, and here is the probability of finding the electron.
I hope now the physical significance of PSI Square, that is probability density is clear.
Josh?