So now we know that probability of finding a particle within a certain range is PSI multiplied by PSI
conjugate, which is even called s PSI Square, and we just went through the probability density definition.
Now, what exactly do we mean by a probability?
We've already seeing this that probability is equal to.
The event.
Which we are trying to predict its probability divided by the total number of outcomes.
See if you apply the probability rule.
In the case of say.
Probability of finding a particular particle is equal to say, multiplied by, say, conjugate, divided
by the whole volume where that particle could be discovered.
Which is nothing but the whole space.
So if we multiply or divide, say, by any constant.
Beyond that is the probability is going to remain the same.
So what exactly is normalization?
And how exactly we do the normalization.
It's very simple, you take that state divided by road.
And so what is this group in and how basically it's applied on normal vectors, which is very much similar
to say, let's check it out.
There is a terminology called auto normal.
Now we know two things that is orthogonal and normal.
What do you mean by an orthogonal, let's say, take two vectors is equal to two, i.e. plus three,
minus K and B is equal to three, A plus plus nine.
Now, if you do the DOT product of A and B, it is equal to zero.
That means that they are orthogonal or perpendicular to each other.
And both are unit vectors as well.
So here you can see.
The example of a unit vector whose value is nothing but one, this is how Unit Vector is calculated,
will see the unit vectors more in depth in the chapter of vectors.
But I think this example should be clearer enough to tell you that what exactly a unit vector looks
like.
So when both the above conditions are met, that is when aid or B is equal to zero.
And when both are unit vectors.
The two actors are said to be auto normal.
That is, you have the property of orthogonal plus normal, and that's why you don't make us our two
normal.
The same terminology applies in SCI as well.
So if you see over here, let's say we have two states or two state vectors, Sivan and Cyto.
Now if the DOT product of both of them is zero and if both are unit vectors.
They are called us or to normal.