# Hybridisation and Variation theory [Quantum Mechanics]

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In summary, there are three commonly used methods for finding approximate solutions to the Schrödinger's equation for complex systems. These include perturbation theory, variation theory, and hybridisation. Variation theory involves modifying the wave equations of fundamental systems, while hybridisation is a technique used to combine states of atoms and molecules. Perturbation theory is used to minimize the energy eigenvalue by varying the linear coefficients.
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## Homework Statement

Give examples of methods used to find approx. answers to the Schrödinger's eqn. of systems too complex to be solved analytically.

None required.

## The Attempt at a Solution

I understand there are three methods commonly used, those mentioned in the title and a 3rd, perturbation theory (of which i can explain) however variation and hybridisation have me at a loss. I've tried many internet sources and my local physics library has no books available.

From what i understand Variation Theory envolves modifying the wave equations of fundamental systems used to describe a system (fundamental systems being things like the rigid rotor, harmonic oscillator, hydrogen-like atom etc.)

Hybridisation however i have less knowledge of, from the name i imagine its something to do with combining states of atoms/molecules.

Actually i just found something on Variation theory, it's used to minimize the energy eigenvalue by varying the linear coefficients.

Just hybridisation i can't find information on now :(

## 1. What is hybridisation theory in quantum mechanics?

Hybridisation theory is a concept in quantum mechanics that explains how atomic orbitals combine to form new hybrid orbitals with different shapes and energies. These hybrid orbitals are used to describe the bonding in molecules and can help predict the molecular geometry and properties of compounds.

## 2. What is the significance of hybridisation theory?

Hybridisation theory is essential for understanding the bonding and structure of molecules. It allows us to explain the observed properties of compounds and predict their behavior in chemical reactions. It also helps in rationalizing the reactivity and stability of molecules.

## 3. How does hybridisation theory relate to variation theory?

Hybridisation theory and variation theory are closely related concepts in quantum mechanics. Variation theory is used to determine the best approximation of the wave function for a system, while hybridisation theory explains how atomic orbitals combine to form hybrid orbitals, which are used in the wave function approximation. Both theories are important in understanding the electronic structure and properties of molecules.

## 4. How does hybridisation theory explain the bonding in molecules?

According to hybridisation theory, when atoms bond to form molecules, their atomic orbitals combine to form new hybrid orbitals. These hybrid orbitals have different shapes and energies from the original atomic orbitals and can overlap with other orbitals to form bonds. The type of hybrid orbitals formed determines the type of bonding in the molecule, such as sigma or pi bonds.

## 5. Can hybridisation theory be applied to all molecules?

No, hybridisation theory is most commonly used for describing the bonding in organic molecules, such as carbon compounds. It can also be applied to certain inorganic molecules, but not all. The applicability of hybridisation theory depends on the types of elements and their electronic configurations present in the molecule.

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