Internal rotation kinetic energy operator

Click For Summary
SUMMARY

The discussion focuses on formulating the kinetic energy operator for internal rotation in molecules, specifically using ethane as an example. It emphasizes that the kinetic energy operator is dependent on the internal degrees of freedom and involves angular momentum operators aligned with the principal axes of inertia. The total angular momentum operator is a key component in this formulation. For further understanding, a reference to a relevant lecture note is provided.

PREREQUISITES
  • Understanding of molecular rotational dynamics
  • Familiarity with angular momentum operators
  • Knowledge of internal coordinates in molecular systems
  • Basic grasp of quantum mechanics principles
NEXT STEPS
  • Study the formulation of kinetic energy operators in quantum mechanics
  • Learn about angular momentum operators in polyatomic molecules
  • Explore the concept of principal axes of inertia in molecular rotation
  • Review lecture notes on molecular dynamics, such as those from the provided link
USEFUL FOR

Chemists, physicists, and students studying molecular dynamics, particularly those interested in quantum mechanics and the rotational behavior of polyatomic molecules.

Konte
Messages
90
Reaction score
1
Hello everybody,

My question today is:
Given a molecule that has an internal degree of liberty ( let's take the ethane molecule with its internal rotation as an example), how to write the kinetic energy operator by means of the corresponding internal coordinate?

Thank you guys.

Konte
 
Physics news on Phys.org
  • Like
Likes   Reactions: Konte
DrClaude said:
It depends on the internal degree of freedom. Rotation of polyatomic molecules involves angular momenta operators along each of the principle axes of inertia, usually rewritten in terms of the total angular momentum operator.

See, e.g., http://tiger.chem.uw.edu.pl/staff/tania/WykladyBJ/Wyklad_ENG_9.pdf

Thank you for answer.
 

Similar threads

Undergrad Molecular Hamiltonian - Ammonia
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Will the kinetic energy operator change with a variable shift?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Kinetic and Potential energy operators commutation
  • · Replies 14 ·
Replies
14
Views
7K
Undergrad Potential energy of spin anti-alignment
  • · Replies 14 ·
Replies
14
Views
4K
Undergrad Quantum thermodynamics of single particle
  • · Replies 13 ·
Replies
13
Views
2K
Internal energy of a gas and kinetic energy, "typical velocity"
  • · Replies 5 ·
Replies
5
Views
1K
Undergrad Identification of changes in internal energy with work (in Callen's Thermodynamics)
  • · Replies 5 ·
Replies
5
Views
1K
Graduate Is the rotational KE of a rigid body considered as internal energy?
  • · Replies 30 ·
2
Replies
30
Views
4K
Graduate Internal forces converting kinetic into potential energy (vice versa)
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad The proportion of kinetic energy of a rotating rigid body?
  • · Replies 7 ·
Replies
7
Views
2K