Hamiltonian of a particle moving on the surface of a sphere

In summary, the conversation discusses a Hamiltonian for a particle of spin 1 constrained to move on the surface of a sphere of radius R. The Hamiltonian is found to be ##H=\frac{\omega}{\hbar}L^2##, which can also be expressed as ##H=\frac{L^2}{2mR^2}##. The participants question the validity of this equality and how it can be proven. Ultimately, it is concluded that ##\omega## is just a parameter with dimensions of ##s^{-1}## that is equal to ##\frac{\hbar}{2mR^2}##.
  • #1
Salmone
101
13
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?
 
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  • #2
As you write yourself, it's just a definition for a parameter ##\omega##. So what should be right or wrong with it?
 
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  • #3
@vanhees71 So ##\omega## is just a parameter which should be equal to ##\frac{\hbar}{2mR^2}## and with dimensions ##s^{-1}##
 
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