Some Explanation with Rigid Rotator

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Discussion Overview

The discussion revolves around the concept of a "Rigid Rotator" in the context of physics, particularly focusing on its implications in rotational systems and the transformation of coordinates in quantum mechanics. Participants seek clarification and deeper understanding of the topic, including its mathematical representation and practical examples.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • One participant requests clarification on whether "Rigid Rotator" refers to a specific application, such as a helicopter rotor.
  • Another participant explains that in the context of a rigid rotor, the radius (r) is constant while the angles (θ and φ) vary.
  • A participant discusses the challenges of solving Schrödinger's eigenvalue equation in Cartesian coordinates and suggests that polar coordinates are more suitable for describing rotational motion.
  • There is a request for a step-by-step explanation of the transformation from Cartesian to polar coordinates, particularly in relation to the Hamiltonian and angular momentum.
  • One participant expresses dissatisfaction with the level of explanation provided and requests a more detailed understanding, including examples related to the rigid rotator concept.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the level of explanation required for the rigid rotator concept, with some seeking more detailed clarification and examples, while others provide initial insights into the topic.

Contextual Notes

The discussion highlights the need for further elaboration on the mathematical aspects and practical implications of the rigid rotator, indicating that participants may have varying levels of familiarity with the topic.

Who May Find This Useful

Students preparing for physics examinations, particularly those studying quantum mechanics and rotational dynamics, may find this discussion relevant.

firoz.raj
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Can anybody explain me .About Rigid Rotator.Kindly let me know the idea.Any help would be
highly appreciated.
 
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I doubt that I can be of any help to you, but I have a request for clarification. Are you referring to a helicopter rotor set, or something else?
 
Welcome to PF!

firoz.raj said:
Can anybody explain me .About Rigid Rotator.Kindly let me know the idea.Any help would be
highly appreciated.

Hi firoz.raj! Welcome to PF! :smile:

Yes, you really do need to be more specific.

What do you mean by "Rigid Rotator"? :confused:​
 


i need to Understood the following Expression.Kindly let me know step by step.

In most respects the analysis of rotational systems is largely a generalization of the types of coordinates used to describe the system. Schrödinger's eigenvalue equation given above is very hard to solve in Cartesian coordinates because motions in the x,y, and z directions are not independent of each other. Polar coordinates most directly describe rotational motion and allow the Hamiltonian to be separated into independent coordinates. For example, the angular velocity is only dependent on the time derivative of the phi coordinate. To solve Schrödinger's equation we need to convert the Hamiltonian to polar coordinates. Chain rule differentiation provides the means for converting differential operators from Cartesian to polar coordinates.

Angular momentum is a vector quantity that results from the cross-product of the position vector r from the center of rotation with the linear momentum vector p of the particles in motion. Conversion of the angular momentum vector to polar coordinates is given in the following table.

For a rigid rotor r is a constant and the Hamiltonian becomes
 

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ok, I understand now. :smile:

"rigid rotor" simply means that r is constant, and only θ and φ vary.

So when we transform from Cartesian to polar coordinates, ∂/∂r = zero, and every ∂/∂r can be omitted, leaving only ∂/∂θ and ∂/∂φ, as shown in your picture.
 
rigid rotor" simply means that r is constant, and only θ and φ vary.

Sir,
i need to Give BS(Physics) Final Year examination.i think this is not a Appropriate Explanation
in My Case.Simple r is Const.and only θ And φ will be vary.i need Good Explanation.Sorry this
is really small question but i will ask.Additional if possible kindly tell me any example also for
Rigid Rotator.
 

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