- #1
Konte
- 90
- 1
Hello everybody,
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.
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.