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A special problem constrain me to make a variable change in my Hamiltonian operator, so with the kinetic energy operator, I have a doubt.

The variable change is: ## \theta \longrightarrow (\theta + k) ## (where ##k## is a constant).

And the kinetic energy operator change as :

$$ \hat{T}_{old}=\frac{-\hbar^2}{2m} \frac{\partial}{\partial \theta^2} \,\, \longrightarrow \,\, \hat{T}_{new}=\frac{-\hbar^2}{2m} \frac{\partial}{\partial (\theta+k)^2} $$

When ##\hat{T}_{old}## and ##\hat{T}_{new}## operate respectively onto a function, say ##\psi(\theta)##, will I have two different results?

Thank you very much.

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# I Kinetic energy operator

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