In classical physics, if we have.
The current state information, and when I see the state information, it's basically the inputs in
this case led to position and momentum with the help of these two input attributes.
We can derive the future speed using Newton's law and Hamilton's equation.
For example, let's take the example of this pendulum.
Let's see, the pendulum at the moment is in position X at this particular time.
Now, after five seconds or ten seconds, if we want to derive or predict the speed of pendulum that
where it has reached.
Then basically, if we know the position and the momentum and we have the equation ready, then we can
birame the future state.
After a certain interval of that particular pendulum.
Similarly, in quantum mechanics, the state of any physical system is given by a state vector, say.
Position X and Time Dimpy.
In Hilbert space.
So what exactly is Hilbert's base?
Let me elaborate.
You can take any actor in three dimensional space.
And it can be formed with the sort of real numbers are and unit vectors I g and get.
As you can see over here, I've written a letter to I play three plus four game.
We can say that this particular vector can be formed with real numbers and you need three vectors like
I g and not only this vector, you take any vector in the universe, it can be formed with real numbers.
And Unit three vectors I g and get.
Let me give you a very easy example to understand Hilbert space, and let's take a fictional story.
Let's say William Shakespeare once met Einstein and told him.
Do you know how beautiful my poems are?
Now, Einstein, being a physicist, could have an analytical brain.
Einstein replied, I never find any beauty in any poem.
Because I get bored with it.
And for your kind information, I have a book.
In which all podiums exist and even in future, what all poems would be written also exists.
And then he gave a dictionary to Shakespeare.
As the dictionary consists of all words which are there in the poems.
You can call a dictionary the Hilbert space.
Hope it's clear now, Josh.