LCSphysicist
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- Homework Statement
- All below
- Relevant Equations
- Schrodinger equation in spherical coordinates.
When solving the Schrödinger equation by separation of variables to atom with one electron and in the spherical coordinates, we get $$\Psi = \Theta(\theta)\phi(\varphi)R(r)$$
Specifically, $$\phi = e^{im\rho }$$
The question is, why we adopt this particular solution, in general, we have this options too:
$$\phi = e^{-im\rho } ; sin(m\rho) ; cos(m\rho)$$
I am trying to see what is the problem with the other.
All are univoc, continuous... (actually, we can make it be continuous is better to say!)
Actually, i would say this:
$$cos(m\rho)$$ changes nothing, but is boring deal with.
$$e^{-im\rho }$$ is like to measure the angle clockwise, unnecessary.
$$sin(m\rho)$$ ... nothing too?
Specifically, $$\phi = e^{im\rho }$$
The question is, why we adopt this particular solution, in general, we have this options too:
$$\phi = e^{-im\rho } ; sin(m\rho) ; cos(m\rho)$$
I am trying to see what is the problem with the other.
All are univoc, continuous... (actually, we can make it be continuous is better to say!)
Actually, i would say this:
$$cos(m\rho)$$ changes nothing, but is boring deal with.
$$e^{-im\rho }$$ is like to measure the angle clockwise, unnecessary.
$$sin(m\rho)$$ ... nothing too?