Quantum Mechanics: Derivations

In this post, we will provide you the basic derivations with a brief explanation of all the important derivations which will come under the Btech Cse 1st semester syllabus.

First, I start with the equation of Compton Effect. In this effect a wavelength strike through the particle and creates a new wavelength. Next we have Schrodinger equation and it is very important derivation. It is defined in 2 forms and they are time-dependent and time-independent forms. Also we have a phase velocity and group velocity and its relation.
T1 derivations

The derivation of one-dimensional potential box and three-dimensional potential are one of the easiest derivation which you will easily write in the papers.
1D box
3D box

Now we have the largest derivation in semester 1 and that is Potential barrier. But first you have to know what it is. It is based on the phenomena of Tunneling effect.
The quantum mechanical penetration of the particle to the potential barrier even when the energy is less than the height of the barrier is called tunneling effect.
Potential_barrier

Next we have another main derivation which is very impressive and contains lots of mathematics and it is rigid rotator.  Rotator
After this you may be probably think "how hard this topic is" or "where can I practice for this derivation", so guys here you can do all the practice and understand this concept: numericals

Another big derivation which is present in our syllabus is the Schrodinger equation for Hydrogen Atom : H2_atom

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