Hybridisation and Variation theory [Quantum Mechanics]

Click For Summary
SUMMARY

This discussion focuses on methods for approximating solutions to the Schrödinger equation in complex systems, specifically highlighting Variation Theory and Hybridisation. Variation Theory modifies wave equations of fundamental systems such as the rigid rotor and harmonic oscillator to minimize energy eigenvalues. Hybridisation involves combining atomic or molecular states, although specific details were less explored in the discussion. Perturbation Theory was also mentioned as a common method for these approximations.

PREREQUISITES
  • Understanding of Schrödinger equation
  • Familiarity with quantum mechanics fundamentals
  • Knowledge of wave functions and energy eigenvalues
  • Basic concepts of atomic and molecular structure
NEXT STEPS
  • Research "Variation Theory in Quantum Mechanics" for detailed methodologies
  • Explore "Hybridisation in Quantum Chemistry" to understand atomic state combinations
  • Study "Perturbation Theory in Quantum Mechanics" for additional approximation techniques
  • Examine "Applications of Schrödinger Equation in Complex Systems" for practical examples
USEFUL FOR

Students of quantum mechanics, physicists exploring complex systems, and researchers interested in approximation methods for the Schrödinger equation.

Distr0
Messages
10
Reaction score
0

Homework Statement



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

Homework Equations



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.
 
Physics news on Phys.org
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 :(
 

Similar threads

Electric sinusoidal field on a hydrogen atom - Quantum Mechanics
  • · Replies 3 ·
Replies
3
Views
2K
A Process of Successive Approximations
  • · Replies 2 ·
Replies
2
Views
2K
Spin-Orbit Coupling in Hydrogen Atom: Understanding the Calculation
  • · Replies 6 ·
Replies
6
Views
4K
QM time independent perturbation theory
  • · Replies 1 ·
Replies
1
Views
2K
Spacetime translations and general Lagrangian density for Field Theory
  • · Replies 5 ·
Replies
5
Views
3K
Degeneracy and non degeneracy in quantum mechanics
  • · Replies 2 ·
Replies
2
Views
1K
Programs Where did all the “fundamentals-deepening” master’s programs go?
  • · Replies 5 ·
Replies
5
Views
652
QFT for Gifted Amateur - Problem 2.2
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Why is m_j not a good quantum number in strong-field Zeeman effect?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad One does not “prove” the basic principles of Quantum Mechanics
  • · Replies 116 ·
4
Replies
116
Views
5K