Chemical Science Short Notes: Variation Method! (Download PDF)

By Renuka Miglani|Updated : November 30th, 2021

Hello Aspirants,

Are you looking for some short and reliable notes during your CSIR-NET preparations? Then, you have come to a perfect place!

Candidates preparing for their CSIR NET exam might need to get some short study notes and strategies to apply while preparing for the key exam of their life. At this point, We at Byjus Exam Prep come up with short notes on the Variation Method, which comes under the Physical Chemistry section of the Chemical Science syllabus.

Our experienced subject matter experts have meticulously designed this set of short notes on the Variation Method to give you the most standard set of study materials to be focused upon. In this cut-throat competitive world, students need to prepare themselves with the best study materials to help them learn and for their future. So, here we are offering the best study notes that are reliable and can be used by the students during their preparations for the upcoming CSIR-NET 2021 exam.

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VARIATION METHOD (Download PDF)

The approximate method based on the variation theorem is known as the Variation Method. It is a method of checking and improving the guesses in the form of trial wave functions (trial) for the complex systems whose exact solution is not possible or not known.

The appropriate trial wavefunction is chosen and it is assumed to be the solution of Schrodinger equation. However, the chosen trial wavefunction may not necessarily be the eigen function of the Schrodinger equation but it must be as close as possible to the true wavefunction. The trial wavefunction is written with a few adjustable parameters, and therefore, we can calculate the energy of the system (Ea) with the trial wave function.

The trial energy (Ea) corresponding to the trial wavefunction is calculated as:

where Ea ≥ E0 (Exact ground state energy).

If the trial wavefunction is normalised, then the denominator of the above equation reduces to unity (condition for normalisation) and hence Ea becomes

It is mandatory that under any condition, the trial energy (Ea) must always be greater or equal to the exact ground state energy (E0).

When the trial wave function matches the true wave function then

Ea = E0

Otherwise, trial energy corresponding to the trial wavefunction is always greater than the exact ground state energy corresponding to the true wavefunction.

So,

Ea > E0

Therefore, by combining the two equations we get

Ea ≥ E0
However, if a number of guesses (trials) are made with corresponding trial energies (Ea) as

then, selection of the better trial wavefunction goes to the corresponding trial energy which follows the two conditions, which are:

(a) Ea ≥ E0

(b) If a set of trial energies follow the above condition (Ea ≥ E0) then further selection is done by choosing the energy closest to the E0 (exact ground state energy).

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