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
"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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