# Hamiltonian of a particle moving on the surface of a sphere

• I
Salmone
In a quantum mechanical exercise, I found the following Hamiltonian:

Consider a particle of spin 1 constrained to move on the surface of a sphere of radius R with Hamiltonian ##H=\frac{\omega}{\hbar}L^2##. I knew that the Hamiltonian of a particle bound to move on the surface of a sphere was ##H=\frac{L^2}{2mR^2}## and then to get the same Hamiltonian should be ##\omega=\frac{\hbar}{2mR^2}## which dimensionally fits, but is it right? How can this equality be proved?

## Answers and Replies

Science Advisor
Gold Member
2022 Award
As you write yourself, it's just a definition for a parameter ##\omega##. So what should be right or wrong with it?

Salmone
Salmone
@vanhees71 So ##\omega## is just a parameter which should be equal to ##\frac{\hbar}{2mR^2}## and with dimensions ##s^{-1}##

Last edited:
vanhees71