Friday, August 14, 2009

Do you have a little time for QM?


Do you have a little time for QM?
Ok, please say, Bismillah.
There are some conceptual things that you should know
I think by now you have heard some stuff about Particle-Wave duality
Now tell me your idea about that
Ok, tell me an example of the particle nature of light
It is so common
Have you seen any experiment in which we observe the momentum of light?

Now let's focus on real issues
The fact is that this Particle-wave dualty is some how nonsense
It is not true to say that the nature of light is particles or waves
Light is light
Some times we use the Particle Model
Some times we use the wave model

As I told you it is just a model
Physicst try to apply it
So far it was quite a useful model
What is it about?
You know physicist main job is to predict future
In classical mechanics we do it using newton equations
If you have F then you have the second derivative of your particle
And from it you compute Velocity and then Position at a later time
Now here you have the schrodinger equation
But it talks about first derivative
And it is alos a complex values function
You have psi
which is your wave
Wave here is only a model
nothing more nothing less
 d psi / dt  is related to laplacian of psi
Ok, do you know what is the H operator?
The hamiltonian operator?

Its simply on operator which gives you the energy of your wave
In quantum Mechanics we have a model named WAVE
But some times we need to MEASURE it
So every Measurement is an Operator and Vice Versa
Yes even measurments in laboratory are Operators
Please don't be confused and don't forget that it is all definitions
Reality is just out there
We should have models
The Operator which gives you the total energy of your wave is the Hamiltonian Operator
As you can see it is simply the first derivative of your wave in respect to time
mulitiplyed by  i * h_bar
Ok, that is for the left side of the schrodinger equation
Which gives you the total energy
But the total energy is a sum of Kinetic energy and Potential energy
The left is the H operator
On the right we have the Kinetic energy
and the Potential energy
The kinetic energy is the  Laplacian operator
and the Potential energy is V(r)
Now you can understand a little more that equation
Just like f=ma this is an empirical equation
It is simply correct
Or better to say it is simply useful

Allah is Al-ʿAlīm, The All Knowing, The Omniscient.


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